Constructing finitely presented monoids which have no finite complete presentation

DOI10.1007/BF02676612zbMath0876.20035OpenAlexW2058817145MaRDI QIDQ1357103

Masashi Katsura, Yuji Kobayashi

Publication date: 7 October 1997

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/135529

zbMATH Keywords

word problemirreducible elementsfinitely presented monoidscomplete rewriting systemspresentations of monoids

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Semigroups in automata theory, linguistics, etc. (20M35)

Related Items (3)

Algebra and geometry of rewriting ⋮ On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids ⋮ Homotopy reduction systems for monoid presentations

Cites Work

• Unnamed Item
• A finitely presented monoid which has solvable word problem but has no regular complete presentation
• For groups the property of having finite derivation type is equivalent to the homological finiteness condition \(FP_ 3\)
• Complete rewriting systems and homology of monoid algebras
• Word problems and a homological finiteness condition for monoids
• A finiteness condition for rewriting systems
• Finite derivation type implies the homological finiteness condition \(FP_ 3\)
• A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier)
• The Knuth-Bendix Completion Procedure and Thue Systems

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