Paper Contents
Abstract
Let R be a ring of order p such that p is a prime number, and p 3. A clean element x of R is an element that can be written as a sum of an idempotent and a unit of R. A ring R is clean if all its elements are clean. A clean graph of a ring Cl(R) is graph whose vertices are of the form (e, u) where e is an idempotent and u is a unit in R and two vertices (e, u) and (f, v) are connected if and only if either ef 0 or uv vu 1 .In this paper, we study some graph theoretic properties of Cl(R) for commutative unitary rings of prime order Keywords; Idempotent, Unit, Clean element, Clean graph
Copyright
Copyright © 2024 Usman Liman Mammawa. This is an open access article distributed under the Creative Commons Attribution License.
Paper ID:
IJPREMS41100038533
ISSN:
2321-9653
Publisher:
ijprems