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Noetherian Semigroup Algebras

✍ Scribed by Eric Jespers; Jan Okniński

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
135 KB
Volume
218
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 Noetherian if and only if w x K S is left Noetherian, or equivalently S satisfies the ascending chain condition on Ž . right left ideals. The latter condition is completely described in terms of the structure of S: in case G is a nilpotent group the quotient group H of S contains a normal subgroup F such that HrF is abelian-by-finite and F : S. Finally, also prime Goldie contracted semigroup algebras are described.

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