منابع مشابه
Strongly nil-clean corner rings
We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings, then $R/J(R)$ is nil-clean. In particular, under certain additional circumstances, $R$ is also nil-clean. These results somewhat improves on achievements due to Diesl in J. Algebra (2013) and to Koc{s}an-Wang-Zhou in J. Pure Appl. Algebra (2016). ...
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In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
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A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_n(R,sigma)$ be the skew triangular matrix ring over a local ring $R$ where $sigma$ is an endomorphism of $R$. We show that $T_2(R,sigma)$ is strongly clean if and only if for any $ain 1+J(R), bin J(R)$, $l_a-r_{sigma(b)}: Rto R$ is surjective. Furt...
متن کاملSome classes of strongly clean rings
A ring $R$ is a strongly clean ring if every element in $R$ is the sum of an idempotent and a unit that commutate. We construct some classes of strongly clean rings which have stable range one. It is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.
متن کاملExtensions of strongly alpha-reversible rings
We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7208