A Multiplicative Dual Nil Q-Clean Rings
نویسندگان
چکیده
In this paper our goal to thoroughly determine the rings in which each non-unit element is a product of nilpotent and quasi-idempotent.
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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The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...
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ژورنال
عنوان ژورنال: Erzincan University Journal of Science and Technology
سال: 2022
ISSN: ['1307-9085', '2149-4584']
DOI: https://doi.org/10.18185/erzifbed.1083173