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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


Semigroup Algebras and Noetherian Maxima
✍ Eric Jespers; Jan Okniński 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 220 KB

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

Noetherian Semigroup Algebras
✍ Eric Jespers; Jan Okniński 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 135 KB

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

Gelfand-Kirillov Dimension of Noetherian
✍ J. Okninski 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 664 KB

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

Semigroup Algebras That Are Principal Id
✍ Eric Jespers; Jan Okniński 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 275 KB

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