In this paper we describe when a monoid algebra K S is a noetherian PI domain which is a maximal order. Our work relies on the study of the height one w x primes of K S and of the minimal primes of the monoid S and leads to a characterization purely in terms of S. It turns out that the primes P inte
Eric Jespers and Jan Okniński: Noetherian Semigroup Algebras
✍ Scribed by John Fountain
- Book ID
- 105927994
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 156 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0037-1912
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📜 SIMILAR VOLUMES
It is shown that a semigroup S is finitely generated whenever the semigroup w x algebra K S is right Noetherian and has finite Gelfand᎐Kirillov dimension or S is a Malcev nilpotent semigroup. If, furthermore, S is a submonoid of a finitely w x generated nilpotent-by-finite group G, then K S is right
It is shown that for certain classes of semigroup algebras \(K[S]\), including right noetherian algebras, the Gelfand-Kirillov dimension is finite whenever it is finite on all cancellative subsemigroups of \(S\). Moreover, the dimension of the algebra modulo the prime radical is then an integer. A d
It is shown that a semigroup algebra K S which is a principal left ideal ring is a finitely generated PI-algebra of Gelfand᎐Kirillov dimension at most 1. A complete Ž . w x description of principal left and right ideal rings K S , and of the underlying w x semigroups S, is obtained. Semiprime princi