Piecewise prime property of skew inverse Laurent series rings and related rings.

Let R be an arbitrary ring equipped with an automorphism α and an α-derivation δ. In this paper, we study on the relationship between the piecewise prime property of a ring R and these of the skew inverse Laurent series ring R((x−1; α,δ)) and related rings. Furthermore, for a piecewise prime ring, we determine a large class of rings which have a generalized triangular matrix representation for which the diagonal rings are prime. Our results extend and unify many available results. Examples for illustration and delimitation of the theory are provided. [ABSTRACT FROM AUTHOR]