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

Abstract

 Let $R$ be an arbitrary ring equipped with an automorphism $\alpha$

and an $\alpha$-derivation $\delta$. 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};

\alpha,\delta))$ 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.