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

Let [Formula: see text] be an arbitrary ring equipped with an automorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. In this paper, we study on the relationship between the piecewise prime property of a ring [Formula: see text] and these of the skew inverse Laurent series ring [Formula: see text] 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.