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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