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Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $\omega: S\rightarrow {\rm End}(R)$ 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 $\overline{\Gamma}(R[[S,\omega ]])$. 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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참고문헌 (34)
참고문헌 신청
D. D. Anderson / 1993 / Beck’s coloring of a commutative ring / J. Algebra 159 (2) : 500 ~ 514
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 434 ~ 447
D. F. Anderson / 2007 / On the diameter and girth of a zero-divisor graph / J. Pure Appl. Algebra 210 (2) : 543 ~ 550
D. S. Passman / 1977 / The Algebraic Structure of Group Rings / Wiley
E. Hashemi / 2005 / Polynomial extensions of quasi-Baer rings / Acta Math. Hungar 107 (3) : 207 ~ 224
D. F. Anderson / 1999 / The zero-divisor graph of a commutative ring / J. Algebra 217 (2) : 434 ~ 447
D. F. Anderson / 2007 / On the diameter and girth of a zero-divisor graph / J. Pure Appl. Algebra 210 (2) : 543 ~ 550
D. S. Passman / 1977 / The Algebraic Structure of Group Rings / Wiley
E. Hashemi / 2005 / Polynomial extensions of quasi-Baer rings / Acta Math. Hungar 107 (3) : 207 ~ 224
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