On Armendariz Rings of Inverse Skew Laurent Series Type.

Let R be a ring equipped with an automorphism α and an α-derivation δ. We study Armendariz rings of inverse (α,δ)-skew Laurent series type ((α,δ)-홸홻홰 rings) as a generalization of the standard Armendariz condition from polynomials to inverse skew Laurent series. We resolve the structure of (α,δ)-홸홻홰 rings and obtain various necessary or sufficient conditions for a ring to be (α,δ)-홸홻홰, unifying and generalizing a number of known Armendariz-like conditions. Also, we study relations between the set of annihilators in R and the set of annihilators in the inverse skew Laurent series ring R((x-1;α,δ)). For an α-compatible (α,δ)-홸홻홰 ring R, we prove that several properties transfer between R and R((x-1;α,δ)). Moreover, the radical of R((x-1;α,δ)) is determined in an α-compatible (α,δ)-홸홻홰 ring R. [ABSTRACT FROM AUTHOR]