Gelfand-Kirillov Dimension of Noetherian Semigroup Algebras

✍ Scribed by J. Okninski

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 664 KB
• Volume: 162
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1993.1255

✦ Synopsis

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 description of cancellative semigroups of polynomial growth, extending Gromov's theorem, has been recently obtained by Grigorchuk. Some bounds on (G K(K[S])) are determined. Our approach is based on the structure of the image (\bar{S}) of (S) modulo the prime radical of (K[S]), on the correspondence between the cancellative subsemigroups in (S) and (S) and on Grigorchuk's result. 1993 Academic Press. Inc.