Geodesic
Note on weakly nil clean and π-regular rings
Filomat, Tome 37 (2023) no. 10, p. 3191

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DOI

Let R be a commutative ring with identity 1 0. The ring R is called weakly nil clean if every element x of R can be written as x = n + e or x = n − e, where n is a nilpotent element of R and e is an idempotent element of R. The ring R is called weakly nil neat if every proper homomorphic image of R is weakly nil clean. Among other results, this paper gives some new characterizations of weakly nil clean (resp. weakly nil neat) rings. An element x ∈ R is said to be von Neumann regular if x = x 2 y for some y ∈ R, and x is said to be π-regular if x n = x 2n y for some y ∈ R and some integer n ≥ 1. It is proved that an element x ∈ R is π-regular if and only if it can be written as x = n + r, where n is a nilpotent element and r is a von Neumann regular element. In this paper, we study the uniqueness of this expression.
DOI : 10.2298/FIL2310191A
Classification : 13A15, 13A99
Keywords: Weakly nil clean rings, π-regular rings 
Khaled Alhazmy; Fuad Ali Ahmed Almahdi; El Mehdi Bouba; Mohammed Tamekkante. Note on weakly nil clean and π-regular rings. Filomat, Tome 37 (2023) no. 10, p. 3191 . doi: 10.2298/FIL2310191A
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     title = {Note on weakly nil clean and \ensuremath{\pi}-regular rings},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2310191A/}
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