Strongly 2T - Clean Rings

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 - S...

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Bibliographic Details
Main Authors: Zeina Hamady, Nazar Shuker
Format: Article
Language:English
Published: Mosul University 2024-12-01
Series:Al-Rafidain Journal of Computer Sciences and Mathematics
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Online Access:https://csmj.uomosul.edu.iq/article_185897_389dd624a1523266b0e16077ac1d2d70.pdf
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Summary: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.
ISSN:1815-4816
2311-7990