TRIANGULAR MATRIX REPRESENTATION OF SKEW GENERALIZED POWER SERIES RINGS

Abstract

Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End (R) a monoid homomorphism. In this paper, we study the triangular matrix representation of skew generalized power series ring R[[S, ω]] which is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev–Neumann rings and generalized power series rings. We investigate that if R is S-compatible and (S, ω)-Armendariz, then the skew generalized power series ring has same triangulating dimension as R. Furthermore, if R is a PWP ring, then skew generalized power series is also PWP ring.