Presentations for semigroups and semigroupoids

Kambites, Mark (2005) Presentations for semigroups and semigroupoids. International Journal of Algebra and Computation, 15 (2). pp. 291-308. ISSN 0218-1967

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We consider the relationship between the combinatorial properties of semigroupoids in general and semigroups in particular. We show that a semigroupoid is finitely generated [finitely presentable] exactly if the corresponding categorical-at-zero semigroup is finitely generated [respectively, finitely presentable]. This allows us to extend some of the main results of [17], to show that finite generation and presentability are preserved under finite extension of semigroupoids and the taking of cofinite subsemigroupoids. We apply this result to extend the results of [6], giving characterizations of finite generation and finite presentability in Rees matrix semigroups over semigroupoids.

Item Type: Article
Uncontrolled Keywords: Semigroups; semigroupoids; generators; relations; presentations; Rees matrix semigroups
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Ms Lucy van Russelt
Date Deposited: 30 Sep 2006
Last Modified: 20 Oct 2017 14:12

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