Al-Rafidain Journal of Computer Sciences and Mathematics (Dec 2024)

Strongly 2T - Clean Rings

  • Zeina Hamady,
  • Nazar Shuker

DOI
https://doi.org/10.33899/csmj.2024.150032.1128
Journal volume & issue
Vol. 18, no. 2
pp. 101 – 104

Abstract

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An element a in a ring R is referred to be strongly 2T-clean (2 – STC element for short), a = Ω-Λ+u, where Ω,Λ are idempotent elements and u is a unit elements of order three. A ring R is considered to be 2 - STC ring if every member of R are 2 - STC ring. This paper presents the idea of an strongly 2T-clean ring and lists some of its fundamental characteristics. Further more we consider 2 - STC ring with 3 is nilpotent, we demonstrate that this ring is equivalent to strongly 2- nil clean ring and the Jacobson radical and the right singular ideal of such ring with 3 is nilpotent is a nil ideal. Finally we exhibit that if R is an 2 - STC ring and if 2 is nilpotent, then a^4-a is nilpotent for every a in R. We domonstrale that if R is 2 - STC ring, then a∈R such that a = Ω-h+u, Ω is idempotent, h is a unit of order two and u is a unit of order three.

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