Stable rank of corner rings

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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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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2004

ISSN: 0002-9939,1088-6826

DOI: 10.1090/s0002-9939-04-07773-1