Results 21 to 30 of about 273,234 (253)
STRONGLY CLEAN POWER SERIES RINGS [PDF]
Proceedings of the Edinburgh Mathematical Society, 2007 AbstractAn element $a$ in a ring $R$ with identity is called strongly clean if it is the sum of an idempotent and a unit that commute. And $a\in R$ is called strongly $\pi$-regular if both chains $aR\supseteq a^2R\supseteq\cdots$ and $Ra\supseteq Ra^2\supseteq\cdots$ terminate.
Jianlong Chen, Yiqiang Zhou
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The strong nil-cleanness of semigroup rings
Open Mathematics, 2020 In this paper, we study the strong nil-cleanness of certain classes of semigroup rings. For a completely 0-simple semigroup M=ℳ0(G;I,Λ;P)M={ {\mathcal M} }^{0}(G;I,\text{Λ};P), we show that the contracted semigroup ring R0[M]{R}_{0}{[}M] is ...
Ji Yingdan
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A NOTE ON STRONGLY *-CLEAN RINGS
, 2015 . A ∗ -ring R is called (strongly) ∗ -clean if every element of R is the sum of a projection and a unit (which commute with each other). In this note, some properties of ∗ -clean rings are considered.
Jian Cui, Zhou Wang
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On strongly nil clean rings [PDF]
Communications in Algebra, 2016 ABSTRACTA ring R is strongly nil clean if every element in R is the sum of an idempotent and a nilpotent that commutes. We prove, in this article, that a ring R is strongly nil clean if and only if for any a ∈ R, there exists an idempotent e ∈ ℤ[a] such that a − e ∈ N(R), if and only if R is periodic and R∕J(R) is Boolean, if and only if each prime ...
Huanyin Chen, Marjan Sheibani
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Left-Right Cleanness and Nil Cleanness in Unital Rings
Известия Иркутского государственного университета: Серия "Математика", 2019 We introduce the notions of left and right cleanness and nil cleanness in rings showing their close relationships with the classical concepts of cleanness and nil cleanness.
P. V Danchev
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Strongly clean matrices over arbitrary rings
Journal of Algebra, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diesl, Alexander J., Dorsey, Thomas J.
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Tripotents: a class of strongly clean elements in rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Periodic elements in a ring generate special classes of strongly clean elements. In particular, elements b such that b = b3+, which are called tripotents and include idempotents, negative of idempotents and order 2 units, are strongly clean.
Călugăreanu Grigore
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Rings in which elements are the sum of a nilpotent and a root of a fixed polynomial that commute
Open Mathematics, 2017 An element in a ring R with identity is said to be strongly nil clean if it is the sum of an idempotent and a nilpotent that commute, R is said to be strongly nil clean if every element of R is strongly nil clean. Let C(R) be the center of a ring R and g(
Handam Ali H., Khashan Hani A.
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A Note on Commutative Nil-Clean Corners in Unital Rings
Известия Иркутского государственного университета: Серия "Математика", 2019 We shall prove that if $R$ is a ring with a family of orthogonal idempotents $\{e_i\}_{i=1}^n$ having sum $1$ such that each corner subring $e_iRe_i$ is commutative nil-clean, then $R$ is too nil-clean, by showing that this assertion is actually ...
P.V. Danchev
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Strongly clean matrix rings over commutative local rings
Journal of Pure and Applied Algebra, 2008 Throughout \(R\) is an associative ring with identity. A ring is called strongly clean if every element is the sum of an idempotent and a unit that commute with each other. The authors completely characterize the commutative local rings \(R\) for which the matrix ring \(\mathbb{M}_n(R)\) is strongly clean, in terms of factorization in \(R[t]\).
Borooah, Gautam +2 more
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