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

Axtell, Michael; Stickles, Joe; Bloome, Lane; Donovan, Rob; Milner, Paul; Peck, Hailee; Richard, Abigail; Williams, Tristan

Involve 8, No. 1, 87-98 (2015).

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

Keywords:

commutative ring with identity; radical ideal; zero-divisor graph; ideal-divisor graph