Chain conditions in commutative rings / / Ali Benhissi

• Autore: Benhissi Ali
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (529 pages)
• Disciplina: 512.4
• Soggetto topico: Commutative rings - Chain conditions; Anells commutatius
• Soggetto genere / forma: Llibres electrònics
• Note generali: Includes index.
• 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.
• Titolo autorizzato: Chain Conditions in Commutative Rings
• ISBN: 9783031098987; 9783031098970
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996495170803316
• Lo trovi qui: Univ. di Salerno