ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS

Abstract

Let be an automorphism of a ring R. The authors (On skew inverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1) (2012) 138-156) applied the concept of Armendariz rings to inverse skew Laurent series rings and introduced skew inverse Laurent-serieswise Armendariz rings. In this article, we study on a special type of these rings and introduce strongly Armendariz rings of inverse skew power series type. We determine the radicals of the inverse skew Laurent series ring R((x 1 ;)), in terms of those of R. We also prove that several properties transfer between R and the inverse skew Laurent series extension R((x 1 ;)), in case R is a strongly Armendariz ring of inverse skew power series type.