Results 1 to 10 of about 60,182 (167)
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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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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Nantong Daxue xuebao. Ziran kexue ban, 2022 A *-ring R is called a medium *-clean ring if every element in R is the sum or difference of a nilpotent with a projection that commute. Fundamenta properties of such *-rings are obtained.
ZHANG Xixi; WU Jun
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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.
Kör, Arda, Ulucak, Gülşen
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On Clean and Nil-Clean Symbolic 2-Plithogenic Rings [PDF]
Neutrosophic Sets and Systems, 2023 A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a
P. Prabakara, Florentin Smarandache
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Bi-amalgamated algebra with (n; p)-weakly clean like properties
Ratio Mathematica, 2023 Let f : A −→ B and g : A −→ C be two ring homomorphisms and let K and K′ be two ideals of B and C, respectively such that f −1(K) = g−1(K′). In this paper, we give a characterization for the bi-amalgamation of A with (B, C) along (K, K′) with respect to (
A Aruldoss, Selvaraj Chelliah
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Strongly Nil* Clean Ideals [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2022 An element is known a strongly nil* clean element if a=e1 - e1e2 + n , where e1,e2 are idempotents and n is nilpotent, that commute with one another.
Muayad Alali, Nazar Shuker
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Journal of Algebra and Its Applications, 2015 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 ...
Chen H., Kose H., Kurtulmaz, Y.
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Mathematics Interdisciplinary Research, 2023 In this paper, we offer a new generalization of the neat ring that is called a w-neat ring. A ring $ R $ is said to be weakly clean if every $ r\in R $ can be written as $ r=u+e $ or $ r=u-e $ where $ u\in$ U$(R) $ and $ e\in$ Id$(R) $.
Fatemeh Rashedi
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p-clean properties in amalgamated rings
Ratio Mathematica, 2023 Let A be a ring. Then A is called p-clean ring if each element in A express as the sum of an idempotent and pure element. Let f : A → B be a ring homomorphism and J be an ideal of B.
SelvaGanesh T, Selvaraj C
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