Height-One Prime Ideals in Semigroup Algebras Satisfying a Polynomial Identity
✍ Scribed by Eric Jespers; Qiang Wang
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 120 KB
- Volume
- 248
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
For a submonoid S of a torsion-free abelian-by-finite group, we describe the height-one prime ideals of the semigroup algebra K S . As an application we investigate when such algebras are unique factorization rings. 2002 Elsevier Science (USA)
Let S be a submonoid of a group. In this paper we investigate when prime semigroup algebras K S are unique factorization rings that satisfy a polynomial identity. In the case S is a group, Chatters showed that this is the case precisely when S is a dihedral free group which satisfies the ascending chain condition on cyclic subgroups. Chatters' result is fundamentally based on an earlier result of Brown [2], who characterized group algebras of polycyclic-by-finite groups that are unique factorization rings. The mentioned results can be extended to arbitrary unique factorization coefficient rings (see ). In the case S is a commutative monoid, Gilmer in described when K S is a unique factorization domain. This paper 118