# ZERO DIVISOR GRAPHS OF SKEW GENERALIZED POWER SERIES RINGS

• MOUSSAVI, AHMAD (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University) ;
• PAYKAN, KAMAL (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
• Published : 2015.10.31

#### Abstract

Let R be a ring, (S,${\leq}$) a strictly ordered monoid and ${\omega}$ : S ${\rightarrow}$ End(R) a monoid homomorphism. The skew generalized power series ring R[[S,${\omega}$]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper, we investigate the interplay between the ring-theoretical properties of R[[S,${\omega}$]] and the graph-theoretical properties of its zero-divisor graph ${\Gamma}$(R[[S,${\omega}$]]). Furthermore, we examine the preservation of diameter and girth of the zero-divisor graph under extension to skew generalized power series rings.

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