On Weakly 2-Invo Clean Rings With Some Properties in Graph Theory

Salim Ghadeer Salim, Raida Dawood Mahmood and Ahmed Mohammed Ali

International Journal of Mathematics and Mathematical Sciences, 2025, vol. 2025, 1-11

Abstract: The concept of a weakly two-involution clean ring is presented; it is a generalization of two-involution clean ring, which allows the addition of more elements to a ring, which will be observed in its graph theoretic representation. The element in a weakly two-involution clean ring can be expressed as a sum or difference of two elements, which is an involution and an idempotent. Furthermore, if the involution and idempotent can be taken such that they commute, the ring is called a strongly weakly two-involution clean ring. We give some properties of weakly two-involution clean rings. It is also proven that R is isomorphic to all from Z3 or Z5 or Z7 when R is a weakly two-involution clean ring with 2 belonging to the set of all unit elements in R. In addition, this paper contains several results related to graph theory, including the connectedness, diameter, girth, and order of a complete subgraph of the graphs resulting from a weakly two-involution clean ring.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:3682352

DOI: 10.1155/ijmm/3682352

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