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A Generalization Of Regular And Strongly $��$-regular Rings
2019We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical von Neumann regular rings and of the strongly $ $-regular rings. Some other close relationships with certain well-known classes of rings such as $ $-regular rings, exchange rings, clean rings ...
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On Strongly -Regular Rings and Strongly Commuting -Regular Rings
Journal of Garmian University, 2017Abdullah Abdul-Jabbar, Lavan Mustafa
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On strongly \(\pi\)-regular rings and periodic rings
2016A ring R is called normal if every idempotent is central. Let \(P=\{x\in R:\) \(xe=x\) for some idempotent e and \(xy=0\) iff \(ey=0\) for \(y\in R\}\). An element \(x\in R\) is called strongly regular if for some y in R \(x=x^ 2y=yx^ 2\). It is called regular if \(xyx=x\) for some y. It is called \(\pi\)-regular (resp. strongly \(\pi\)-regular) if \(x^
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Tight closure and strongly F-regular rings
Research in Mathematical Sciences, 2022Melvin Hochster
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Strongly Additively Regular Rings and Graphs
2019A commutative ring R is said to be additively regular if for each pair of elements \(f,g\in R\) with f regular, there is an element \(t\in R\) such that \(g+ft\) is regular. For any commutative ring R, the polynomial ring \(R[{\scriptstyle \mathrm {X}}]\) is additively regular, moreover if \(deg(g)
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Some generalizations of strongly regular rings. III
1972A ring A is called a P1-ring if aAa = aA for all a 2 A. The author's main results are the following theorems. Theorem 6: For an arbitrary ring A with no nonzero nilpotent ideals the following two conditions are equivalent: (i) A is a P1 ring, (ii) A is strongly regular (i.e., a 2 a2A for any a 2 A).
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A symmetric generalization of $$\pi $$-regular rings
Ricerche Di Matematica, 2021Peter V Danchev
exaly
Rings derived from strongly $$\mathcal {U}$$ U -regular relations
Boletin De La Sociedad Matematica Mexicana, 2017S Mirvakili, S M Anvariyeh, Bijan Davvaz
exaly
On (Strongly) Gorenstein Von Neumann Regular Rings
Communications in Algebra, 2011Mahdou Najib +2 more
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