Journal ArticleDOI
Nil-clean and strongly nil-clean rings
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In this paper, it was shown that a ring R is strongly nil-clean if it is a sum of an idempotent and a unit that commute and a − a 2 is a nilpotent.About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 2016-02-01. It has received 79 citations till now. The article focuses on the topics: Matrix ring & Jacobson radical.read more
Citations
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A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
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Rings in which every element is a sum of two tripotents
TL;DR: In this article, the authors proved that every element of a ring is a sum of an idempotent and a tripotent that commute if and only if the identity of the tripotent is known.
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On expressing matrices over Z2 as the sum of an idempotent and a nilpotent
TL;DR: In this article, it was shown that for every n × n matrix A over the field Z 2 there exists an idempotent matrix E such that (A − E ) 4 = 0.
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Rings in which elements are sums of nilpotents, idempotents and tripotents
TL;DR: In this article, the authors completely determine the rings for which every element is a sum of a nilpotent, an idempotent and a tripotent that commute with one another.
References
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Book
Rings and Categories of Modules
Frank W. Anderson,Kent R. Fuller +1 more
TL;DR: In this paper, the authors provide a self-contained account of much of the theory of rings and modules, focusing on the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules.
Journal ArticleDOI
A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Book
A first course in noncommutative rings
TL;DR: In this article, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Journal ArticleDOI
Lifting idempotents and exchange rings
TL;DR: In this article it was shown that a projective module P has the finite exchange property if and only if, whenever P = N + M where N and M are submodules, there is a decomposition P = A @ B with A S N and B C M.