Homological Finiteness Conditions for Groups, Monoids, and Algebras

DOI10.1080/00927870600796110zbMath1122.20034arXivmath/0609146OpenAlexW2129837361MaRDI QIDQ3422798

Stephen J. Pride

Publication date: 14 February 2007

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

Full work available at URL: https://arxiv.org/abs/math/0609146

zbMATH Keywords

graded algebrasgroup ringsfree resolutionsmonoid ringshomological finiteness conditionsmonoids of finite homological type

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Ordinary and skew polynomial rings and semigroup rings (16S36) Free semigroups, generators and relations, word problems (20M05) Homological methods in group theory (20J05) Syzygies, resolutions, complexes in associative algebras (16E05) Graded rings and modules (associative rings and algebras) (16W50) Connections of semigroups with homological algebra and category theory (20M50)

Related Items (9)

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 ⋮ Topological finiteness properties of monoids. I: Foundations ⋮ Homological finiteness properties of monoids, their ideals and maximal subgroups. ⋮ The Homological Finiteness Properties Left-, Right-, and Bi-FP_nof Monoids ⋮ Free inverse monoids are not \(\mathrm{FP}_2\) ⋮ On higher order homological finiteness of rewriting systems. ⋮ Equivariant group presentations and the second homology group of the Torelli group ⋮ Semigroups with finitely generated universal left congruence

Cites Work

• Homological dimension and syzygies
• Finiteness conditions on groups and quasi-isometries
• For finitely presented monoids the homological finiteness conditions FHT and \(\text{bi-FP}_3\) coincide
• Homological Finite Derivation Type
• A Monoid which is Right FP _∞ but not Left FP ₁
• ON HOMOTOPICAL AND HOMOLOGICAL FINITENESS CONDITIONS FOR FINITELY PRESENTED MONOIDS
• Gröbner bases of associative algebras and the Hochschild cohomology

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