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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mosul University
2024-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| 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. |
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| ISSN: | 1815-4816 2311-7990 |