Involution t–Clean Rings with Applications

Authors

  • Shaimaa Ahmad University of Mosul, Iraq
  • Mohammed AL-Neima University of Mosul, Iraq https://orcid.org/0000-0002-6591-0123
  • Ahmed Ali University of Mosul, Iraq
  • Raida Mahmood University of Mosul, Iraq

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4530

Keywords:

clean ring, invo-clean ring, tripotent element, Hosoya polynomial, Wiener index

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.

Author Biographies

Shaimaa Ahmad, University of Mosul, Iraq

Mohammed AL-Neima, University of Mosul, Iraq

Ahmed Ali, University of Mosul, Iraq

Raida Mahmood, University of Mosul, Iraq

Downloads

How to Cite

Ahmad, S., AL-Neima, M., Ali, A., & Mahmood, R. . (2022). Involution t–Clean Rings with Applications. European Journal of Pure and Applied Mathematics, 15(4), 1637–1648. https://doi.org/10.29020/nybg.ejpam.v15i4.4530