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http://dx.doi.org/10.4134/CKMS.2015.30.4.363

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)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.4, 2015 , pp. 363-377 More about this Journal
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.
Keywords
zero-divisor graph; diameter; girth; skew generalized power series ring; skew power series ring; reduced ring;
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