Two-sided homological properties of special and one-relator monoids

Gray, Robert D. and Steinberg, Benjamin (2026) Two-sided homological properties of special and one-relator monoids. Forum of Mathematics, Sigma, 14. ISSN 2050-5094

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Abstract

A monoid presentation is called special if the right-hand side of each defining relation is equal to 1. We prove results which relate the two-sided homological finiteness properties of a monoid defined by a special presentation with those of its group of units. Specifically we show that the monoid enjoys the homological finiteness property bi-. Moreover, we show that if r is not a proper power then the one-relator monoid has Hochschild cohomological dimension at most 2, while if r is a proper power then it has infinite Hochschild cohomological dimension. For any nonspecial one-relator monoid M with defining relation u=v we show that if there is no nonempty word w such that u,v ϵ A *w ⋂ w A * then M is of type bi-FP ∞ and has Hochschild cohomological dimension at most 2.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	https://www.scopus.com/pages/publication...
Depositing User:	LivePure Connector
Date Deposited:	18 Mar 2026 10:30
Last Modified:	13 May 2026 08:23
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102394
DOI:	10.1017/fms.2026.10209

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