ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS

Let $alpha$ 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 $R((x^{-1};alpha))$, in terms of those of $R$. We also prove that several properties transfer between $R$ and the inverse skew Laurent series extension $R((x^{-1};alpha))$, in case $R$ is a strongly Armendariz ring of inverse skew power series type.