ON HOMOTOPICAL AND HOMOLOGICAL FINITENESS CONDITIONS FOR FINITELY PRESENTED MONOIDS

DOI10.1142/S0218196701000577zbMath1026.20058OpenAlexW2019231301MaRDI QIDQ4786287

Friedrich Otto, Yuji Kobayashi

Publication date: 15 December 2002

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196701000577

zbMATH Keywords

word problemmonoid presentationsfinitely presented monoidshomotopy typeshomological finiteness conditions

Mathematics Subject Classification ID

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

Related Items (11)

SOME EXACT SEQUENCES FOR THE HOMOTOPY (BI-)MODULE OF A MONOID ⋮ THE HOMOLOGICAL FINITENESS PROPERTY FP₁ AND FINITE GENERATION OF MONOIDS ⋮ For finitely presented monoids the homological finiteness conditions FHT and \(\text{bi-FP}_3\) coincide ⋮ Undecidable properties of monoids with word problem solvable in linear time. II: Cross sections and homological and homotopical finiteness conditions. ⋮ Topological finiteness properties of monoids. I: Foundations ⋮ Higher-dimensional normalisation strategies for acyclicity ⋮ On properties not inherited by monoids from their Schützenberger groups. ⋮ On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids ⋮ Homological Finite Derivation Type ⋮ FINITENESS CONDITIONS FOR REWRITING SYSTEMS ⋮ Homological Finiteness Conditions for Groups, Monoids, and Algebras

Cites Work

• 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)
• String rewriting and homology of monoids
• SECOND ORDER DEHN FUNCTIONS OF GROUPS AND MONOIDS
• LOW-DIMENSIONAL HOMOTOPY THEORY FOR MONOIDS

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