科研之友
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摘要
For a commutative ring R with identity, an ideal-based zero-divisor graph, denoted by (I)(R), is the graph whose vertices are {xR\I|xyIforsomeyR\I}, and two distinct vertices x and y are adjacent if and only if xyI. In this article, we investigate an annihilator ideal-based zero-divisor graph by replacing the ideal I with the annihilator ideal Ann(M) for a multiplication R-module M. Based on the above-mentioned definition, we examine some properties of an R-module over a von Neumann regular ring, and the cardinality of an R-module associated with (Ann(M))(R).
- 出版日期2013-3-6
