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Chain conditions in commutative rings / / Ali Benhissi
| Chain conditions in commutative rings / / Ali Benhissi |
| Autore | Benhissi Ali |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (529 pages) |
| Disciplina | 512.4 |
| Soggetto topico |
Commutative rings - Chain conditions
Anells commutatius |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031098987
9783031098970 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 S-Noetherian Modules and Rings -- 1 S-Noetherian Modules -- 2 S-Noetherian Rings -- 3 Modules Over S-Noetherian Rings -- 4 Polynomials Over S-Noetherian Rings -- 5 Formal Power Series Over S-Noetherian Rings -- 6 S-Noetherian Pull Backs -- 7 S-Noetherian Amalgamations -- 8 Applications -- 9 Polynomials and Formal Power Series with Coefficients in a Module -- 10 S-Noetherian Nagata Rings -- 11 S-Noetherian t-Nagata Rings -- 12 Formal Power Series Over a Krull Domain -- 13 Polynomials Over a Krull Domain -- 14 Formal Power Series Over a Generalized Krull Domain -- Problems -- Solutions -- References -- 2 S-Artinian Rings and Modules -- 1 Saturated Multiplicative Sets of a Ring -- 2 S-Artinian Rings -- 3 S-Artinian Modules -- 4 S-Cofinite Rings and Modules -- 5 Multiplication Modules -- 6 S-Artinian and S-Cofinite Idealization -- 7 Artinian Rings and Modules -- 8 Application to the Theorem of Generalized Principal Ideal -- 9 Nagata's Example -- Problems -- Solutions -- References -- 3 Almost Principal Polynomial Rings -- 1 Generalities -- 2 Applications of Anderson-Kwak-Zafrullah Theorem -- 3 Characterization of A[X] Almost Principal by the Ideals f(X)K[X] A[X] -- 4 Applications to Extensions of Integral Domains -- 5 The Almost Principal Ideals of the Form f(X)K[X]A[X] in the Ring A[X] -- 6 Applications to Semi-Normal Integral Domains -- 7 The Almost Principal Polynomial Rings and the v-Operation -- 8 Generators of the Ideal f(X)K[X]A[X] -- 9 Prestable Ideals -- 10 When Is the Ideal f(X)K[X] A[X] Maximal? -- 11 Application to Goldman Rings -- Problems -- Solutions -- References -- 4 The SFT and t-SFT Rings -- 1 Krull Dimension of the Formal Power Series Ring -- 2 Transfer of the SFT Property to the Amalgamation -- 3 Transfer of the SFT Property to the Polynomial Ring -- 4 J. Coykendall Example (2002).
5 Transfer of the SFT Property to the Formal Power Series Ring -- 6 The I-Adic Topology on Rings -- 7 Infinite Product of Formal Power Series over a Nondiscrete Valuation Domain of Rank One -- 8 The Zeros of Formal Power Series -- 9 Infinite Product of Formal Power Series over an Integral Domain -- 10 Completion of a Metric Space -- 11 Projective Limit of a Projective System of Rings -- 12 Construction of the I-Adic Completion of a Ring -- 13 The I-Adic Completion of a Noetherian Ring -- 14 The I-Adic Completion of a Valuation Domain -- 15 Generalities on the t-SFT Domains -- 16 Transfer of the t-SFT Property to the Polynomial Domain -- 17 Transfer of the t-SFT Property to the t-Flat Over-Rings -- 18 Chains Condition in the t-SFT Domains -- 19 Application to Formal Power Series -- Problems -- Solutions -- References -- 5 Nonnil-Noetherian Rings -- 1 Generalities on Nonnil-Noetherian Rings -- 2 The Nilradical of the Formal Power Series Ring -- 3 Krull's Dimension of the Formal Power Series Ring over a Nonnil-Noetherian Ring -- 4 Transfer of the Nonnil-Noetherian Property to the Ring of Formal Power Series -- 5 Characterization of the Nonnil-Noetherian Property by Formal Power Series -- 6 Nonnil-S-Noetherian Rings -- Problems -- Solutions -- References -- 6 Strongly Hopfian, Endo-Noetherian, and Isonoetherian Rings -- 1 Generalities on the Strongly Hopfian Rings -- 2 The Zero Dimensional Rings -- 3 Auto-Injective Rings -- 4 Product of Zero Dimensional Rings -- 5 Injection in a Zero Dimensional Ring -- 6 Polynomials Over a Strongly Hopfian Ring -- 7 Formal Power Series Over a Strongly Hopfian Bounded Ring -- 8 Formal Power Series Over a Chained Ring -- 9 Formal Power Series Over a Ring with Nonzero Characteristic -- 10 Study of an Example -- 11 Other Criteria for the Strong Hopfianity -- 12 Power Series Armendariz Rings -- 13 Endo-Noetherian Rings. 14 Polynomials and Formal Power Series Over an Endo-Noetherian Ring -- 15 Polynomials and Formal Power Series Over a PF-Ring -- 16 Isonoetherian Valuation Domains -- 17 Isonoetherian Modules -- 18 u-Isonoetherian Extensions of Rings -- 19 Isonoetherian Rings of the Form A+XB[X]/A+XB[[X]] -- 20 Isonoetherian Nagata's Idealization Ring -- Problems -- Solutions -- References -- Index. |
| Record Nr. | UNINA-9910616378503321 |
Benhissi Ali
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chain conditions in commutative rings / / Ali Benhissi
| Chain conditions in commutative rings / / Ali Benhissi |
| Autore | Benhissi Ali |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (529 pages) |
| Disciplina | 512.4 |
| Soggetto topico |
Commutative rings - Chain conditions
Anells commutatius |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031098987
9783031098970 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 S-Noetherian Modules and Rings -- 1 S-Noetherian Modules -- 2 S-Noetherian Rings -- 3 Modules Over S-Noetherian Rings -- 4 Polynomials Over S-Noetherian Rings -- 5 Formal Power Series Over S-Noetherian Rings -- 6 S-Noetherian Pull Backs -- 7 S-Noetherian Amalgamations -- 8 Applications -- 9 Polynomials and Formal Power Series with Coefficients in a Module -- 10 S-Noetherian Nagata Rings -- 11 S-Noetherian t-Nagata Rings -- 12 Formal Power Series Over a Krull Domain -- 13 Polynomials Over a Krull Domain -- 14 Formal Power Series Over a Generalized Krull Domain -- Problems -- Solutions -- References -- 2 S-Artinian Rings and Modules -- 1 Saturated Multiplicative Sets of a Ring -- 2 S-Artinian Rings -- 3 S-Artinian Modules -- 4 S-Cofinite Rings and Modules -- 5 Multiplication Modules -- 6 S-Artinian and S-Cofinite Idealization -- 7 Artinian Rings and Modules -- 8 Application to the Theorem of Generalized Principal Ideal -- 9 Nagata's Example -- Problems -- Solutions -- References -- 3 Almost Principal Polynomial Rings -- 1 Generalities -- 2 Applications of Anderson-Kwak-Zafrullah Theorem -- 3 Characterization of A[X] Almost Principal by the Ideals f(X)K[X] A[X] -- 4 Applications to Extensions of Integral Domains -- 5 The Almost Principal Ideals of the Form f(X)K[X]A[X] in the Ring A[X] -- 6 Applications to Semi-Normal Integral Domains -- 7 The Almost Principal Polynomial Rings and the v-Operation -- 8 Generators of the Ideal f(X)K[X]A[X] -- 9 Prestable Ideals -- 10 When Is the Ideal f(X)K[X] A[X] Maximal? -- 11 Application to Goldman Rings -- Problems -- Solutions -- References -- 4 The SFT and t-SFT Rings -- 1 Krull Dimension of the Formal Power Series Ring -- 2 Transfer of the SFT Property to the Amalgamation -- 3 Transfer of the SFT Property to the Polynomial Ring -- 4 J. Coykendall Example (2002).
5 Transfer of the SFT Property to the Formal Power Series Ring -- 6 The I-Adic Topology on Rings -- 7 Infinite Product of Formal Power Series over a Nondiscrete Valuation Domain of Rank One -- 8 The Zeros of Formal Power Series -- 9 Infinite Product of Formal Power Series over an Integral Domain -- 10 Completion of a Metric Space -- 11 Projective Limit of a Projective System of Rings -- 12 Construction of the I-Adic Completion of a Ring -- 13 The I-Adic Completion of a Noetherian Ring -- 14 The I-Adic Completion of a Valuation Domain -- 15 Generalities on the t-SFT Domains -- 16 Transfer of the t-SFT Property to the Polynomial Domain -- 17 Transfer of the t-SFT Property to the t-Flat Over-Rings -- 18 Chains Condition in the t-SFT Domains -- 19 Application to Formal Power Series -- Problems -- Solutions -- References -- 5 Nonnil-Noetherian Rings -- 1 Generalities on Nonnil-Noetherian Rings -- 2 The Nilradical of the Formal Power Series Ring -- 3 Krull's Dimension of the Formal Power Series Ring over a Nonnil-Noetherian Ring -- 4 Transfer of the Nonnil-Noetherian Property to the Ring of Formal Power Series -- 5 Characterization of the Nonnil-Noetherian Property by Formal Power Series -- 6 Nonnil-S-Noetherian Rings -- Problems -- Solutions -- References -- 6 Strongly Hopfian, Endo-Noetherian, and Isonoetherian Rings -- 1 Generalities on the Strongly Hopfian Rings -- 2 The Zero Dimensional Rings -- 3 Auto-Injective Rings -- 4 Product of Zero Dimensional Rings -- 5 Injection in a Zero Dimensional Ring -- 6 Polynomials Over a Strongly Hopfian Ring -- 7 Formal Power Series Over a Strongly Hopfian Bounded Ring -- 8 Formal Power Series Over a Chained Ring -- 9 Formal Power Series Over a Ring with Nonzero Characteristic -- 10 Study of an Example -- 11 Other Criteria for the Strong Hopfianity -- 12 Power Series Armendariz Rings -- 13 Endo-Noetherian Rings. 14 Polynomials and Formal Power Series Over an Endo-Noetherian Ring -- 15 Polynomials and Formal Power Series Over a PF-Ring -- 16 Isonoetherian Valuation Domains -- 17 Isonoetherian Modules -- 18 u-Isonoetherian Extensions of Rings -- 19 Isonoetherian Rings of the Form A+XB[X]/A+XB[[X]] -- 20 Isonoetherian Nagata's Idealization Ring -- Problems -- Solutions -- References -- Index. |
| Record Nr. | UNISA-996495170803316 |
|
Benhissi Ali
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
| Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (898 pages) |
| Disciplina | 512.24 |
| Soggetto topico |
Àlgebra commutativa
Anells commutatius Commutative algebra |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030896942
9783030896935 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466556503316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
| Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (898 pages) |
| Disciplina | 512.24 |
| Soggetto topico |
Àlgebra commutativa
Anells commutatius Commutative algebra |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030896942
9783030896935 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910547291403321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Graphs from rings / / David F. Anderson [and three others]
| Graphs from rings / / David F. Anderson [and three others] |
| Autore | Anderson David F. <1948-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (548 pages) : illustrations |
| Disciplina | 511.5 |
| Soggetto topico |
Graph theory
Commutative rings Algebra Anells commutatius Teoria de grafs |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-88410-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Notation -- Contents -- Chapter 1 Introduction -- 1.1 Basics in Algebra -- 1.2 Basics in Graph Theory -- Chapter 2 Distances in Zero-divisor Graphs -- 2.1 Zero-divisor Graphs -- 2.2 Basic Properties of Zero-divisor Graphs -- 2.3 Girth of Zero-divisor Graphs -- 2.3.1 Rings of Polynomials and Power Series -- 2.3.2 Idealization -- 2.3.3 Rings with Linearly Ordered Primes -- 2.4 Diameter of Zero-divisor Graphs -- 2.4.1 Rings of Polynomials and Power Series -- 2.4.2 Idealization -- 2.4.3 Rings with Linearly Ordered Primes -- 2.5 Radius and Center of Zero-divisor Graphs -- 2.6 Rings without Identity -- Chapter 3 Properties of Zero-divisor Graphs -- 3.1 Coloring of Zero-divisor Graphs -- 3.1.1 Vertex Coloring -- 3.1.2 Clique Number -- 3.1.3 Edge Coloring -- 3.2 Connectivity of Zero-divisor Graphs -- 3.3 Isomorphisms and Automorphisms -- 3.4 Bipartite Zero-divisor Graphs -- 3.5 Zero-divisor Graphs of Gaussian Integers -- 3.6 Cycles in Zero-divisor Graphs -- 3.6.1 Trees and Complements -- 3.6.2 Eulerian and Hamiltonian Graphs -- Chapter 4 Genus of Zero-divisor Graphs -- 4.1 Genus of Graphs -- 4.2 Planar Zero-divisor Graphs -- 4.3 Zero-divisor Graphs with Genus One -- 4.4 Zero-divisor Graphs with Genus Two -- 4.5 Zero-divisor Graphs with Large Genus -- 4.6 Crosscap of Zero-divisor Graphs -- 4.7 Embedding of Line Graphs -- Chapter 5 Generalized Zero-divisor Graphs -- 5.1 Ideal-based Zero-divisor Graphs -- 5.2 Properties of ΓI(R) -- 5.2.1 Clique Number of Ideal-based Zero-divisor Graphs -- 5.3 Genus of Ideal-based Zero-divisor Graphs -- 5.4 Primal Ideal-based Zero-divisor Graphs -- 5.5 Annihilating-ideal Graphs -- 5.6 Special Annihilating-ideal Graphs -- 5.7 Coloring of Annihilating-ideal Graphs -- 5.8 Genus of Annihilating-ideal Graphs -- 5.9 Compressed Zero-divisor Graphs -- 5.9.1 Properties of Compressed Zero-divisor Graphs.
5.9.2 Girth of Compressed Zero-divisor Graphs -- 5.10 Extended Zero-divisor Graphs -- Chapter 6 Zero-divisor Graph Generalizations -- 6.1 Noncommutative Rings -- 6.1.1 Directed Zero-divisor Graphs of Finite Rings -- 6.2 Commutative Semigroups -- 6.3 Commutative Semirings -- 6.4 Modules -- 6.4.1 Torsion Graphs of Modules -- 6.4.2 Zero-divisor Graphs of Modules -- 6.4.3 Annihilator Ideal-based Graphs of Modules -- 6.5 Domination in Directed Zero-divisor Graphs -- Chapter 7 Total Graphs of Commutative Rings -- 7.1 Definition of Total Graph -- 7.2 Basic Properties of Total Graphs -- 7.3 Polynomial Rings and Idealization -- 7.4 Properties of Total Graphs -- 7.4.1 Eulerian and Hamiltonian Graphs -- 7.4.2 Colorings -- 7.4.3 Connectivity -- 7.4.4 Domination -- 7.4.5 Intersection Graphs of Dominating Sets -- 7.5 Genus of Total Graphs -- Chapter 8 Graphs from Total Graphs -- 8.1 Total Graphs without the Zero Element -- 8.1.1 Basic Properties -- 8.1.2 Zero-divisor Paths and Regular Paths -- 8.2 The Regular Graph -- 8.3 Complements of Total Graphs -- 8.4 Generalized Complements of Total Graphs -- 8.5 Line Graphs of Total Graphs -- Chapter 9 Generalized Total Graphs -- 9.1 Commutative Ring Generalizations -- 9.1.1 Ideal-based Generalized Total Graphs -- 9.1.2 Total Graphs of Multiplicatively Closed Sets -- 9.1.3 Total Graphs of Multiplicative-prime Sets -- 9.2 Total Graphs of Modules -- 9.2.1 Total Torsion Element Graphs -- 9.2.2 Total Graphs of Modules -- 9.3 Commutative Semirings -- 9.3.1 Total Graphs of Semirings -- 9.3.2 Identity Summand Graphs -- Chapter 10 Other Graphs Associated with Rings -- 10.1 Graphs of Commutative Rings -- 10.1.1 Cayley Graphs -- 10.1.2 Co-maximal and Unit Graphs -- 10.1.3 Cozero-divisor Graphs -- 10.1.4 Jacobson and Intersection Graphs -- 10.2 Annihilator Graphs -- 10.2.1 Equal Annihilator and Zero-divisor Graphs. 10.3 Compressed Annihilator Graphs -- 10.4 ΓI(R), ΓI(R), and AGI(R) -- 10.5 Congruence-based Graphs -- 10.6 Element Graphs -- 10.7 Dot Product Graphs -- 10.7.1 Subgraphs of Dot Product Graphs -- 10.7.2 Equivalence Dot Product Graphs -- 10.8 Trace Graph of Matrices -- 10.8.1 Basic Properties of Trace Graphs -- 10.8.2 Planarity and Thickness of Trace Graphs -- 10.8.3 Domination in Trace Graphs of Matrices -- 10.8.4 Ideal-based Trace Graphs of Matrices -- 10.9 Graphs of Noncommutative Rings -- 10.9.1 Commuting and Non-commuting Graphs -- 10.9.2 Nilpotent and Idempotent Graphs -- 10.10 Graphs of Ideals -- 10.11 Divisor Graphs -- 10.12 Subgroup Graphs of a Group -- Bibliography -- Index. |
| Record Nr. | UNINA-9910508482303321 |
|
Anderson David F. <1948->
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Graphs from rings / / David F. Anderson [and three others]
| Graphs from rings / / David F. Anderson [and three others] |
| Autore | Anderson David F. <1948-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (548 pages) : illustrations |
| Disciplina | 511.5 |
| Soggetto topico |
Graph theory
Commutative rings Algebra Anells commutatius Teoria de grafs |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-88410-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Notation -- Contents -- Chapter 1 Introduction -- 1.1 Basics in Algebra -- 1.2 Basics in Graph Theory -- Chapter 2 Distances in Zero-divisor Graphs -- 2.1 Zero-divisor Graphs -- 2.2 Basic Properties of Zero-divisor Graphs -- 2.3 Girth of Zero-divisor Graphs -- 2.3.1 Rings of Polynomials and Power Series -- 2.3.2 Idealization -- 2.3.3 Rings with Linearly Ordered Primes -- 2.4 Diameter of Zero-divisor Graphs -- 2.4.1 Rings of Polynomials and Power Series -- 2.4.2 Idealization -- 2.4.3 Rings with Linearly Ordered Primes -- 2.5 Radius and Center of Zero-divisor Graphs -- 2.6 Rings without Identity -- Chapter 3 Properties of Zero-divisor Graphs -- 3.1 Coloring of Zero-divisor Graphs -- 3.1.1 Vertex Coloring -- 3.1.2 Clique Number -- 3.1.3 Edge Coloring -- 3.2 Connectivity of Zero-divisor Graphs -- 3.3 Isomorphisms and Automorphisms -- 3.4 Bipartite Zero-divisor Graphs -- 3.5 Zero-divisor Graphs of Gaussian Integers -- 3.6 Cycles in Zero-divisor Graphs -- 3.6.1 Trees and Complements -- 3.6.2 Eulerian and Hamiltonian Graphs -- Chapter 4 Genus of Zero-divisor Graphs -- 4.1 Genus of Graphs -- 4.2 Planar Zero-divisor Graphs -- 4.3 Zero-divisor Graphs with Genus One -- 4.4 Zero-divisor Graphs with Genus Two -- 4.5 Zero-divisor Graphs with Large Genus -- 4.6 Crosscap of Zero-divisor Graphs -- 4.7 Embedding of Line Graphs -- Chapter 5 Generalized Zero-divisor Graphs -- 5.1 Ideal-based Zero-divisor Graphs -- 5.2 Properties of ΓI(R) -- 5.2.1 Clique Number of Ideal-based Zero-divisor Graphs -- 5.3 Genus of Ideal-based Zero-divisor Graphs -- 5.4 Primal Ideal-based Zero-divisor Graphs -- 5.5 Annihilating-ideal Graphs -- 5.6 Special Annihilating-ideal Graphs -- 5.7 Coloring of Annihilating-ideal Graphs -- 5.8 Genus of Annihilating-ideal Graphs -- 5.9 Compressed Zero-divisor Graphs -- 5.9.1 Properties of Compressed Zero-divisor Graphs.
5.9.2 Girth of Compressed Zero-divisor Graphs -- 5.10 Extended Zero-divisor Graphs -- Chapter 6 Zero-divisor Graph Generalizations -- 6.1 Noncommutative Rings -- 6.1.1 Directed Zero-divisor Graphs of Finite Rings -- 6.2 Commutative Semigroups -- 6.3 Commutative Semirings -- 6.4 Modules -- 6.4.1 Torsion Graphs of Modules -- 6.4.2 Zero-divisor Graphs of Modules -- 6.4.3 Annihilator Ideal-based Graphs of Modules -- 6.5 Domination in Directed Zero-divisor Graphs -- Chapter 7 Total Graphs of Commutative Rings -- 7.1 Definition of Total Graph -- 7.2 Basic Properties of Total Graphs -- 7.3 Polynomial Rings and Idealization -- 7.4 Properties of Total Graphs -- 7.4.1 Eulerian and Hamiltonian Graphs -- 7.4.2 Colorings -- 7.4.3 Connectivity -- 7.4.4 Domination -- 7.4.5 Intersection Graphs of Dominating Sets -- 7.5 Genus of Total Graphs -- Chapter 8 Graphs from Total Graphs -- 8.1 Total Graphs without the Zero Element -- 8.1.1 Basic Properties -- 8.1.2 Zero-divisor Paths and Regular Paths -- 8.2 The Regular Graph -- 8.3 Complements of Total Graphs -- 8.4 Generalized Complements of Total Graphs -- 8.5 Line Graphs of Total Graphs -- Chapter 9 Generalized Total Graphs -- 9.1 Commutative Ring Generalizations -- 9.1.1 Ideal-based Generalized Total Graphs -- 9.1.2 Total Graphs of Multiplicatively Closed Sets -- 9.1.3 Total Graphs of Multiplicative-prime Sets -- 9.2 Total Graphs of Modules -- 9.2.1 Total Torsion Element Graphs -- 9.2.2 Total Graphs of Modules -- 9.3 Commutative Semirings -- 9.3.1 Total Graphs of Semirings -- 9.3.2 Identity Summand Graphs -- Chapter 10 Other Graphs Associated with Rings -- 10.1 Graphs of Commutative Rings -- 10.1.1 Cayley Graphs -- 10.1.2 Co-maximal and Unit Graphs -- 10.1.3 Cozero-divisor Graphs -- 10.1.4 Jacobson and Intersection Graphs -- 10.2 Annihilator Graphs -- 10.2.1 Equal Annihilator and Zero-divisor Graphs. 10.3 Compressed Annihilator Graphs -- 10.4 ΓI(R), ΓI(R), and AGI(R) -- 10.5 Congruence-based Graphs -- 10.6 Element Graphs -- 10.7 Dot Product Graphs -- 10.7.1 Subgraphs of Dot Product Graphs -- 10.7.2 Equivalence Dot Product Graphs -- 10.8 Trace Graph of Matrices -- 10.8.1 Basic Properties of Trace Graphs -- 10.8.2 Planarity and Thickness of Trace Graphs -- 10.8.3 Domination in Trace Graphs of Matrices -- 10.8.4 Ideal-based Trace Graphs of Matrices -- 10.9 Graphs of Noncommutative Rings -- 10.9.1 Commuting and Non-commuting Graphs -- 10.9.2 Nilpotent and Idempotent Graphs -- 10.10 Graphs of Ideals -- 10.11 Divisor Graphs -- 10.12 Subgroup Graphs of a Group -- Bibliography -- Index. |
| Record Nr. | UNISA-996466408003316 |
|
Anderson David F. <1948->
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
