Semigroup Algebras That Are Principal Ideal Rings

✍ Scribed by Eric Jespers; Jan Okniński

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 275 KB
• Volume: 183
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0241

✦ Synopsis

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 principal left ideal rings K S are shown to be principal right ideal rings and a description of this class of rings follows.