Monoid kernels and profinite topologies on the free Abelian group

DOI10.1017/S0004972700036571zbMath0946.20041MaRDI QIDQ4940634

Benjamin Steinberg

Publication date: 2 August 2000

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

membership problempointlike setsprofinite topologiesfinite monoidsrational languageslattices of pseudovarietiesrational setsfree Abelian groups of finite rankpseudovarieties of Abelian groups

Mathematics Subject Classification ID

Lattices of varieties (08B15) Varieties and pseudovarieties of semigroups (20M07) Semigroups in automata theory, linguistics, etc. (20M35) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10) Limits, profinite groups (20E18) Torsion-free groups, finite rank (20K15) Topological methods for abelian groups (20K45)

Related Items (11)

Fundamental groups,inverse schützenberger automata,and monoid presentations ⋮ POLYNOMIAL CLOSURE AND TOPOLOGY ⋮ INEVITABLE GRAPHS AND PROFINITE TOPOLOGIES: SOME SOLUTIONS TO ALGORITHMIC PROBLEMS IN MONOID AND AUTOMATA THEORY, STEMMING FROM GROUP THEORY ⋮ COMBINATORIAL GROUP THEORY, INVERSE MONOIDS, AUTOMATA, AND GLOBAL SEMIGROUP THEORY ⋮ Pointlike sets and separation: a personal perspective ⋮ Abelian kernels, profinite topologies and the extension problem ⋮ On the relative solvability of certain inverse monoids. ⋮ Finite state automata: A geometric approach ⋮ A Lower Bound For Reversible Automata ⋮ Every decidable pseudovariety of abelian groups is completely tame ⋮ Computing relative Abelian kernels of finite monoids.

Cites Work

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• Categories as algebra: An essential ingredient in the theory of monoids
• Abelian pointlikes of a monoid
• INEVITABLE GRAPHS: A PROOF OF THE TYPE II CONJECTURE AND SOME RELATED DECISION PROCEDURES
• ASH'S TYPE II THEOREM, PROFINITE TOPOLOGY AND MALCEV PRODUCTS: PART I
• On The Profinite Topology on a Free Group
• THE PRO-p TOPOLOGY OF A FREE GROUP AND ALGORITHMIC PROBLEMS IN SEMIGROUPS
• On Pointlike Sets and Joins of Pseudovarieties

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