Author

# F. H. Abdulqadr

Bio: F. H. Abdulqadr is an academic researcher from Salahaddin University. The author has contributed to research in topics: Maximal ideal & Vertex (geometry). The author has an hindex of 1, co-authored 1 publications receiving 3 citations.

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TL;DR: The notion of maximal ideal graph of a commutative ring with identity was introduced and studied in this article, where the authors introduced the notion of MG(R) and studied its properties and characterizations.

Abstract: In this paper, we introduce and study the notion of the maximal ideal graph of a commutative ring with identity. Let R be a commutative ring with identity. The maximal ideal graph of R, denoted by MG(R), is the undirected graph with vertex set, the set of non-trivial ideals of R, where two vertices I1 and I2 are adjacent if I1 I2 and I1+I2 is a maximal ideal of R. We explore some of the properties and characterizations of the graph.

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TL;DR: In this paper , a new class of rings called involution t-clean ring is introduced which every element in the ring are sum of involution and tripotent elements. And the graph of the ring has diameter one and girth three.

Abstract: A new class of rings are introduced which every element in the ring are sum of involution and tripotent elements. This class called involution t-clean ring which is a generalization of invo-clean rings and subclass of clean rings. Some properties of this class are investigate. For an application in graph theory, new graph is defined called t-clean graph of involution t-clean ring the set of vertices is order pairs of involution and tripotent element which is the sum of them is involution t-clean element. The two vertices are adjacent if and only if the sum of involution elements are zero or the product of the tripotent elements are zero. The graphs are connecting, has diameter one and girth three.