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Hereditary Semigroup Algebras

✍ Scribed by Eric Jespers; Qiang Wang

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 128 KB
Volume: 229
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8227

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✦ Synopsis

In "Semigroup Algebras," Okniński posed the following question: characterize semigroup algebras that are hereditary. In this paper we describe the (prime contracted) semigroup algebras K S that are hereditary and Noetherian when S is either a Malcev nilpotent monoid, a cancellative monoid or a monoid extension of a finite non-null Rees matrix semigroup. Furthermore, for the class of monoids which have an ideal series with factors that are non-null Rees matrix semigroups, we obtain an upper bound for the global dimension of its contracted semigroup algebra.

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