Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem

DOI10.1016/0022-4049(88)90043-6zbMath0679.20056OpenAlexW1966871890MaRDI QIDQ1822636

Susan Lazarus, Karsten Henckell, John L. Rhodes

Publication date: 1988

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(88)90043-6

zbMATH Keywords

infinite Zeiger wreath productPrime Decomposition Theoremtriple Schützenberger product

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Free semigroups, generators and relations, word problems (20M05) Connections of semigroups with homological algebra and category theory (20M50)

Related Items (10)

Pointlike sets and separation: a personal perspective ⋮ Product expansions ⋮ The synthesis theorem for finite regular semigroups, and its generalization ⋮ Residual smallness in commutative algebra ⋮ Algebraic and topological theory of languages ⋮ HOLONOMY EMBEDDING OF ARBITRARY STABLE SEMIGROUPS ⋮ Infinite iteration of matrix semigroups. II: Structure theorem for arbitrary semigroups up to aperiodic morphism ⋮ Pointlike sets: the finest aperiodic cover of a finite semigroup ⋮ Semigroup expansions using the derived category, kernel, and Malcev products ⋮ Merge Decompositions, Two-sided Krohn–Rhodes, and Aperiodic Pointlikes

Cites Work

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• The kernel of monoid morphisms
• Infinite iteration of matrix semigroups. I: Structure theorem for torsion semigroups
• The synthesis theorem for finite regular semigroups, and its generalization
• Pointlike sets: the finest aperiodic cover of a finite semigroup
• Global structure theories for finite semigroups. Introduction. I: Extension of the fundamental theorem of finite semigroups. II: Axioms for complexity for all finite semigroups. III: Complexity of two-\(J\) class semigroups. IV: Synthesis of the classical and modern theory of finite semigroups
• Semigroups and one-way functions

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