Results 1 to 10 of about 276,111 (308)
International Journal of Mathematics and Mathematical Sciences, 2006 In this paper we unify the structures of various clean rings by introducing the notion of P-clean rings. Some properties of P-clean rings are investigated, which generalize the known results on clean rings, semiclean rings, n-clean rings, and so forth ...
Weixing Chen
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Journal of Algebra and Its Applications, 2014 A ring R is feckly clean provided that for any a ∈ R there exists an element e ∈ R and a full element u ∈ R such that a = e + u, eR(1 - e) ⊆ J(R). We prove that a ring R is feckly clean if and only if for any a ∈ R, there exists an element e ∈ R such that V(a) ⊆ V(e), V(1 - a) ⊆ V(1 - e) and eR(1 - e) ⊆ J(R), if and only if for any distinct maximal ...
H. Chen, Handan Köse, Yosum Kurtulmaz
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Symmetrization in Clean and Nil-Clean Rings [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 We introduce and investigate D-clean and D-nil-clean rings as well as some other closely related symmetric versions of cleanness and nil-cleanness. A comprehensive structural characterization is given for these symmetrically clean and symmetrically nil ...
Danchev, Peter Vasilevich
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On Types of Invo Clean Rings: Review [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsIn this paper, three types of rings were reviewed: invo-clean, invo-t-clean and invo-k-clean, the ring invo-clean is invo-t-clean and invo-k-clean. Since invo-t-clean ring is invo-k-clean when k=3.
Mohammed Al-Neima, Raida Mahmood
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.
Călugăreanu Grigore, Pop Horia F.
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On Monochromatic Clean Condition on Certain Finite Rings [PDF]
Mathematics, 2023 For a finite commutative ring R, let a,b,c∈R be fixed elements. Consider the equation ax+by=cz where x, y, and z are idempotents, units, and any element in the ring R, respectively.
Kai An Sim +3 more
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On $ mj $-clean ring and strongly $ mj $-clean ring
Turkish Journal of Mathematics, 2022 Summary: In this paper, we introduce the concepts of \(mj\)-clean and strongly \(mj\)-clean rings which are generalizations of \(j\)-clean ring and strongly \(j\)-clean ring, respectively. Let \(R\) be a ring with a nonzero identity and \(m\geq 2\) a positive integer.
GÜLŞEN ULUCAK, ARDA KÖR
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Weakly Clean Rings and Almost Clean Rings [PDF]
Rocky Mountain Journal of Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Myung-Sook Ahn, D. D. Anderson
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Feebly r-clean ideal and feebly *-r-clean ideal
Ratio Mathematica, 2023 In this article, we introduce the concept of feebly r-clean ring and feebly ∗-r-clean ring. A ring R is defined to be feebly r-clean, if every element a can be written as a = r + e − f, where u is a regular and e, f are orthogonal idempotents and A ...
Saravanan Viswanathan
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On uniquely $\pi$-clean rings [PDF]
Communications in Algebra, 2014 An element of a ring is unique clean if it can be uniquely written as the sum of an idempotent and a unit. A ring $R$ is uniquely $ $-clean if some power of every element in $R$ is uniquely clean. In this article, we prove that a ring $R$ is uniquely $ $-clean if and only if for any $a\in R$, there exists an $m\in {\Bbb N}$ and a central idempotent ...
Huanyin Chen
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