The strongly annihilating-ideal graph of a commutative ring with respect to an ideal

Articles in Press

Document Type : Research Paper

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Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

Abstract

For a commutative ring R with identity, SAG(R) be the graph whose vertices are the nonzero annihilating ideals of R and with two distinct nonzero annihilating ideals I and J joined by an edge when I∩Ann(J)≠(0) and J∩Ann(I)≠(0). Also, strongly Annihilating-ideal graph with respect to an ideal (I), that it is shown by SAGI(R), is the graph whose vertices are all ideals of R such that K⊈I and for some ideal J that J⊈I, KJ⊆I, and distinct vertices K and J are adjacent if and only if J∩AnnI(K)⊈I and K∩AnnI(J)⊈I. In this paper, we study the notion of SAGI(R). Also, among other results, we give some results about the relationships between SAGI(R) and SAG(R/I).
 

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References

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Algebraic Structures and Their Applications

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Available Online from 16 April 2025

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