For finitely presented monoids the homological finiteness conditions FHT and \(\text{bi-FP}_3\) coincide

DOI10.1016/S0021-8693(03)00177-7zbMath1028.20041OpenAlexW2002588691MaRDI QIDQ1399171

Friedrich Otto, Yuji Kobayashi

Publication date: 30 July 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(03)00177-7

zbMATH Keywords

exact sequencesmonoid ringsrewriting systemsrelation bimodulesfinitely generated monoidshomological finiteness conditions FP\(_n\) and bi-FP\(_n\)presentations of finite homological type

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Grammars and rewriting systems (68Q42) Semigroup rings, multiplicative semigroups of rings (20M25) Connections of semigroups with homological algebra and category theory (20M50)

Related Items

THE HOMOLOGICAL FINITENESS PROPERTY FP₁ AND FINITE GENERATION OF MONOIDS ⋮ Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry ⋮ Higher-dimensional normalisation strategies for acyclicity ⋮ Homological finiteness properties of monoids, their ideals and maximal subgroups. ⋮ On some homotopical and homological properties of monoid presentations. ⋮ The Homological Finiteness Properties Left-, Right-, and Bi-FP_nof Monoids ⋮ On properties not inherited by monoids from their Schützenberger groups. ⋮ On higher order homological finiteness of rewriting systems. ⋮ FINITENESS CONDITIONS FOR REWRITING SYSTEMS ⋮ Homological Finiteness Conditions for Groups, Monoids, and Algebras

Cites Work

• Unnamed Item
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• For groups the property of having finite derivation type is equivalent to the homological finiteness condition \(FP_ 3\)
• On universal derivations
• Finite complete rewriting systems and the complexity of word problem
• Word problems and a homological finiteness condition for monoids
• Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings
• A finiteness condition for rewriting systems
• Homological Finite Derivation Type
• RELATION MODULES AND RELATION BIMODULES OF GROUPS, SEMIGROUPS AND ASSOCIATIVE ALGEBRAS
• Diagram groups
• SECOND ORDER DEHN FUNCTIONS OF GROUPS AND MONOIDS
• ON HOMOTOPICAL AND HOMOLOGICAL FINITENESS CONDITIONS FOR FINITELY PRESENTED MONOIDS
• SOME EXACT SEQUENCES FOR THE HOMOTOPY (BI-)MODULE OF A MONOID
• FOR REWRITING SYSTEMS THE TOPOLOGICAL FINITENESS CONDITIONS FDT AND FHT ARE NOT EQUIVALENT
• LOW-DIMENSIONAL HOMOTOPY THEORY FOR MONOIDS