ON SKEW POWER SERIESWISE ARMENDARIZ RINGS

For a ring endomorphism alpha, we introduce and investigate SPA-rings which are a generalization of alpha-rigid rings and determine the radicals of the skew polynomial rings R[x; alpha], R[x, x(-1); alpha] and the skew power series rings R[x; alpha]] R[[x, x(-1); alpha], in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SPA-ring. We will construct various types of nonreduced SPA-rings and show SPA is a strictly stronger condition than alpha-rigid.