Finite derivation type implies the homological finiteness condition \(FP_ 3\)

DOI10.1006/jsco.1994.1039zbMath0834.20065OpenAlexW1997476598MaRDI QIDQ1338340

Friedrich Otto, Robert Cremanns

Publication date: 18 March 1996

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1994.1039

zbMATH Keywords

finitely generated groupsmonoid ringsmonoid presentationsfinite derivation typefinitely generated monoidsrewriting ruleshomological finiteness condition \(FP_ 3\)

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free semigroups, generators and relations, word problems (20M05) Semigroups in automata theory, linguistics, etc. (20M35) Grammars and rewriting systems (68Q42) Homological dimension (category-theoretic aspects) (18G20) Connections of semigroups with homological algebra and category theory (20M50)

Related Items

THE PROPERTY FDT IS UNDECIDABLE FOR FINITELY PRESENTED MONOIDS THAT HAVE POLYNOMIAL-TIME DECIDABLE WORD PROBLEMS, 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, A finiteness condition for rewriting systems, Finite derivation type for Rees matrix semigroups, A Lyndon's identity theorem for one-relator monoids, A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier), FDT is undecidable for finitely presented monoids with solvable word problems, Constructing finitely presented monoids which have no finite complete presentation, Finite derivation type for semi-direct products of monoids, Analysis approach to finite monoids, Homotopy bases and finite derivation type for subgroups of monoids., The next step of the word problem over monoids., Higher-dimensional normalisation strategies for acyclicity, Algebra and geometry of rewriting, The word problem for one-relation monoids: a survey, Homological Finite Derivation Type, THE p-COCKCROFT PROPERTY OF THE SEMI-DIRECT PRODUCTS OF MONOIDS, FINITENESS CONDITIONS FOR REWRITING SYSTEMS, A NEW EXAMPLE FOR MINIMALITY OF MONOIDS, Bottom-up rewriting for words and terms, Finite complete rewriting systems and finite derivation type for small extensions of monoids, Finite homotopy bases of one-relator monoids, Efficiency for self semi-direct products of the free Abelian monoid on two generators., Homotopy reduction systems for monoid presentations, Polygraphs of finite derivation type