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An exploration of ideal-divisor graphs. (English) Zbl 1312.13029

Summary: Zero-divisor graphs have given some interesting insights into the behavior of commutative rings. Redmond introduced a generalization of the zero-divisor graph called an ideal-divisor graph. This paper expands on Redmond’s findings in an attempt to find additional information about the structure of commutative rings from ideal-divisor graphs.

MSC:

13M05 Structure of finite commutative rings
13A99 General commutative ring theory
05C99 Graph theory
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