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36 - M. Behboodi (Joint with F. Aliniaeifard, E. Mehdi-Nezhad and A. M. Rahimi), The annihilating-ideal graph of a commutative ring with respect to an ideal, Comm. Algebra 42 (2014), 2269-2284.(ISI)

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted AG_I(R), is the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices joined by an edge when the product of the vertices is the zero ideal. We will generalize this notion for an ideal I of R by replacing nonzero ideals whose product is zero with ideals that are not contained in I and their product lies in I and call it the annihilating-ideal graph of R with respect to I, denoted AG_I(R). We discuss when AG_I(R)  is bipartite. We also give some results on the subgraphs and the parameters of AG_I(R).

Journal Papers
Month/Season: 
March
Year: 
2014