Semigroups, categories, and partial algebras : ICSAA 2019, Kochi, India, December 9-12 / / P. G. Romeo, Mikhail V. Volkov, A. R. Rajan, editors

• Pubblicazione: Singapore : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (xiv, 241 pages) : illustrations
• Disciplina: 515.724
• Soggetto topico: Semigroups of operators; Operator theory; Partial algebras; Semigrups d'operadors; Teoria d'operadors
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): RomeoP. G.; VolkovMikhail V.; RajanA. R.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- Editors and Contributors -- Ordering Orders and Quotient Rings -- 1 Introduction -- 2 Green's Relations -- 3 Generalized Inverses -- 3.1 Inverses Along an Element -- 3.2 Properties of the Group Inverse -- 4 Order Relations on General Semigroups and Their Properties -- 5 Quotient Rings Along Functions -- 5.1 Properties of Fountain-Gould Quotient Rings -- 6 Order Relations on a Quotient Ring -- 6.1 Mitsch Order Relation -- 6.2 Nambooripad Order Relation -- 6.3 Sharp Order -- References -- A Study on Cayley Graphs of Full Transformation Semigroups -- 1 Introduction -- 2 Preliminaries -- References -- Block-Groups and Hall Relations -- 1 Background and Motivation: Straubing's Theorem -- 2 Block-Groups and Power Semigroups of Groups -- 3 Hall Relations -- 4 Representation Theorem -- References -- Balanced Categories and the Biorder in Semigroups -- 1 Categories with Subobjects, Images, and the Biorders in Semigroups -- 1.1 Morphisms in a Category -- 1.2 Categories with Subobjects -- 1.3 Factorization of Morphisms and Categories with Images -- 2 The Cone Semigroup of a Category and Its Abundance -- 2.1 The Cone Semigroup calBC and the Idempotent Biorder of It -- 2.2 The Cone Semigroup calTcalC and Its Abundance -- 3 The Left Ideal Category of an Abundant Semigroup and Its Cone Semigroup -- 4 The Isomorphism Between Balanced Category calC and mathbbL(calTcalC) -- References -- Category of Principal Left Ideals of Normal Bands -- 1 Preliminaries -- 1.1 Normal Categories -- 1.2 Category of Principal Left Ideals of a Regular Semigroups -- 2 Normal Category from Normal Bands -- 2.1 Normal Bands -- 2.2 Category of Principal Left Ideals of Normal Bands -- References -- Quotients of the Booleanization of an Inverse Semigroup -- 1 Introduction -- 2 Preliminaries -- 2.1 First Definitions and Conventions. ; 2.2 Representations and Proper Representations of Semilattices -- 2.3 The Universal Booleanization of a Semilattice -- 2.4 The Tight Booleanization of a Semilattice -- 2.5 Stone Duality for Boolean Algebras -- 2.6 Boolean Inverse Semigroups -- 2.7 Stone Groupoids -- 2.8 The Universal Groupoid of an Inverse Semigroup -- 2.9 The Tight Groupoid of an Inverse Semigroup -- 2.10 Stone Duality for Boolean Inverse Semigroups -- 3 X-to-Join Representations of Semilattices and Inverse Semigroups -- 3.1 X-to-Join Representations of Semilattices -- 3.2 Connection with π-Tight Representations -- 3.3 X-to-Join Representations of Inverse Semigroups -- 4 Prime and Core Representations -- 5 Generators and Relations -- 6 Weakly Meet-Preserving Quotients of B(S) via X-to-Join Representations -- 7 Intermediate Boundary Quotients of C*-Algebras of Zappa-Szép Product Right LCM Semigroups via X-to-Join Representations -- 7.1 X-to-Join Representations of Inverse Semigroups in C*-Algebras -- 7.2 Right LCM Semigroups and Their Left Inverse Hulls -- 7.3 The C*-Algebra and the Boundary Quotient C*-Algebra of a Right LCM Semigroup -- 7.4 Zappa-Szép Products: A Construction Due to Brownlowe, Ramagge, Robertson, and Whittaker -- 7.5 C*A(UbowtieA) and C*U(UbowtieA) via X-to-Join Representations -- References -- On the Structure of the Commuting Graph of Brandt Semigroups -- 1 Introduction -- 2 Preliminaries -- 3 Main Results -- References -- The Mathematical Work of K. S. S. Nambooripad -- 1 Introduction -- 2 Regular Semigroups, Biordered Sets, and Inductive Groupoids -- 3 Outgrowths of Nambooripad's Inductive Groupoid Approach -- 4 Regular Semigroups and Cross-Connections -- 5 Outgrowths of Nambooripad's Cross-Connection Theory -- 6 Connections Between Regular Semigroups and Other Areas -- 7 Ph.D. Theses Directed by Nambooripad -- References. ; Markov Chains Through Semigroup Graph Expansions (A Survey) -- 1 Introduction -- 2 Stationary Distribution from Semigroup Expansions -- 2.1 Markov Chains -- 2.2 Right Cayley Graphs -- 2.3 The Karnofsky-Rhodes Expansion -- 2.4 The McCammond Expansion -- 2.5 Stationary Distribution -- 2.6 Loop Graphs -- 2.7 Kleene Expressions -- 2.8 From Kleene Expressions to Rational Functions -- 2.9 Mixing Time -- 2.10 Another Example -- References -- On Various Multiplicity-Free Products of Schur Functions -- 1 Introduction -- 2 Terminology and Notation -- 3 Multiplicity-Free Outer and Kronecker Products of Irreducible Characters -- 4 Multiplicity-Free Plethysms of Schur Functions -- References -- On ω-Identities over Finite Aperiodic Semigroups with Commuting Idempotents -- 1 Introduction -- 2 ω-Identities -- 3 The Automaton of an ω-Term -- 4 Reversible Aperiodic Quotient of an Automaton -- 5 The ω-Word Problems over AcapECom and AInv -- References -- The Polycyclic Inverse Monoids and the Thompson Groups Revisited -- 1 Introduction -- 2 The Thompson Groups via the Polycyclic Inverse Monoids -- 2.1 The Distributive Inverse Monoid Dn -- 2.2 The Group Associated with a Polycyclic Inverse Monoid -- 3 The Structure of Prefix Codes -- 4 The Tight Completion -- 4.1 The Lenz Congruence equiv -- 4.2 The Structure of the Lenz Congruence on Dn -- 4.3 Handling Right-Infinite Strings -- 4.4 The Boolean Inverse Monoid Cn -- 5 The n-Ary Cantor Algebra -- 5.1 A Restriction Monoid -- 5.2 n-Ary Cantor Algebras -- 5.3 The 1-Generated Case -- References -- Category of Chain Bundles -- 1 Preliminaries -- 2 Category of Chain Bundles -- 3 Category of Preorder Chains -- 4 Some Categorical Properties of Chain Bundles -- References -- Cancellable Elements in the Lattice of Overcommutative Semigroup Varieties -- 1 Introduction -- 2 Preliminaries and Summary -- 3 G-Sets. ; 4 The Structure of the Lattice mathbbOC -- 5 Proof of Theorem2.2 -- References.
• Altri titoli varianti: ICSAA 2019
• Titolo autorizzato: Semigroups, categories, and partial algebras
• ISBN: 981-334-842-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910484242103321
• Lo trovi qui: Univ. Federico II
• Serie: Springer proceedings in mathematics & statistics ; ; Volume 345.