Global Journal of Pure and Applied Mathematics

  • Year: 2009
  • Volume: 5
  • Issue: 1

Associativity of Some Skew Semigroup Rings

  • Author:
  • B. Tabatabaie Shourijeh
  • Total Page Count: 9
  • DOI:
  • Page Number: 31 to 39

Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71454, Iran,.

Abstract

Given a partial action α of a discrete group G on an associative algebra A. The notion of skew group ring A×αG, corresponding to α is introduced by M. Dokuchaev and R. Exel in [1] where the associativity of A×αG is proved for a semiprime algebra A. We generalize this idea to an action of a unital inverse semigroup S on an arbitrary C* -algebra A. Also, we introduce the notion of skew semigroup ring A×βS and we prove its associativity without using approximate identity.

Keywords

C* -algebra, partial action, partial automorphism, skew group ring