Results 11 to 20 of about 3,954 (230)
Note on weakly nil clean and π-regular rings
Filomat, 2023 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,
Khaled Alhazmy +3 more
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Weakly Semicommutative Rings and Strongly Regular Rings
Kyungpook mathematical journal, 2014 A ring R is called weakly semicommutative ring if for any a, b ∈ R∗ = R \ {0} with ab = 0, there exists n ≥ 1 such that either a = 0 and aRb = 0 or b = 0 and aRb = 0. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if
Long Wang, Junchao Wei
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Left prime weakly regular near-rings
Tamkang Journal of Mathematics, 2005 In this paper we introduce the notion of left prime weakly regular, left primeweakly $ \pi $-regular and left prime pseudo $ \pi $-regular near-rings. We alsointroduce the concept of strong left prime weakly regular near-rings. We haveobtained conditions for a near-ring $ N $ to be left prime pseudo $ \pi $-regular.We have also obtained conditions for ...
Dheena, P., Sivakumar, D.
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On Weakly Tripotent and Locally Invo-Regular Rings
, 2023 In this article some important observations have been reported on recent works related to weakly tripotent rings and locally invo-regular rings. Our findings give additional results as well as correct some recent results on weakly tripotent rings and locally invo-regular rings appeared in Rendiconti Sem. Mat. Univ. Pol.
S K Pandey
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Extension of Weakly and Strongly F-Regular Rings by Flat Maps [PDF]
Journal of Algebra, 2001 Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We investigate the conditions under which the weak or strong F-regularity of R passes to S. We show that is suffices that the closed fiber S/mS be Gorenstein and either F-finite (if R and S have a common test element), or F-rational (otherwise).
Ian M. Aberbach
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On Weakly von Neumann regular rings [PDF]
, 2009 In this paper, we define and study a particular case of von Neumann regular notion called a weak von Neumann regular ring. It shown that the polynomial ring $R[x]$ is weak von Neumann regular if and only if $R$ has exactly two idempotent elements. We provide necessary and sufficient conditions for $ R=A\propto E $ to be a weak von Neumann ring.
Kabbour, Mohammed, Mahdou, Najib
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Applicable Algebra in Engineering, Communication and Computing, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Celik, Dilek, Ozbudak, Ferruh
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Journal of Pure and Applied Algebra, 2006 It is well known that weak regularity is equivalent to regularity and biregularity for left Artinian rings. In this paper the authors prove the following result: for a ring \(R\) satisfying the ACC on right annihilators, if \(R\) is left weakly regular then \(R\) is biregular, and that \(R\) is left weakly regular if and only if \(R\) is a direct ...
Hong, Chan Yong +4 more
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When rings of continuous functions are weakly regular [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2015 It is well known that, for any Tychonoff space \(X\), the ring \(C(X)\) is regular in the sense of von Neumann precisely when \(X\) is a \(P\)-space. This result also holds in the broader context of pointfree topology. Indeed, denoting the ring of real-valued continuous functions on a frame \(L\) by \(\mathcal RL\), then \(\mathcal RL\) is a regular ...
Dube, Themba, Nsayi, Jissy Nsonde
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weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings [PDF]
, 2018 Let R be a commutative ring with identity.
Anderson, David F. +2 more
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