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2006.382: Presentations for semigroups and semigroupoids

2006.382: Mark Kambites (2005) Presentations for semigroups and semigroupoids. International Journal of Algebra and Computation, 15 (2). pp. 291-308. ISSN 0218-1967

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DOI: 10.1142/S0218196705002268

Abstract

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 2000 > 18 Category theory; homological algebra
MSC 2000 > 20 Group theory and generalizations
MIMS number:2006.382
Deposited By:Miss Louise Stait
Deposited On:30 September 2006

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