on annihilator properties of inverse skew power series rings

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse skew power series type. we determine the radicals of theinverse skew laurent series ring $r((x^{-1};alpha))$, in terms ofthose 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 ofinverse skew power series type.