Results 11 to 20 of about 276,111 (308)
Miskolc Mathematical Notes, 2015 Summary: Let \(C(R)\) denote the center of a ring \(R\) and \(g(x)\) be a polynomial of ring \(C(R)[x]\). An element \(r\in R\) is called ``\(g(x)\)-clean'' if \(r=s+u\) where \(g(s)=0\) and \(u\) is a unit of \(R\) and \(R\) is \(g(x)\)-clean if every element is \(g(x)\)-clean.
Ashrafi, Nahid, Ahmadi, Zahra
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On Weakly 2-Invo Clean Rings With Some Properties in Graph Theory [PDF]
International Journal of Mathematics and Mathematical SciencesThe concept of a weakly two-involution clean ring is presented; it is a generalization of two-involution clean ring, which allows the addition of more elements to a ring, which will be observed in its graph theoretic representation.
Salim Ghadeer Salim +2 more
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Strongly 2T - Clean Rings [PDF]
Al-Rafidain Journal of Computer Sciences and MathematicsAn element a in a ring R is referred to be strongly 2T-clean (2 – STC element for short), a = Ω-Λ+u, where Ω,Λ are idempotent elements and u is a unit elements of order three.
Zeina Hamady, Nazar Shuker
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Mathematical Reports, 2017 "A ring R is Yaqub nil-clean if a+a3 or a−a3 is nilpotent for all a ∈ R. We prove that a ring R is a Yaqub nil-clean ring if and only if R ∼= R1,R2,R3,R1 ×R2 or R1×R3, where R1/J(R1) is Boolean, R2/J(R2) is a Yaqub ring, R3/J(R3) ∼= Z5 and each J(Ri) is nil, if and only if J(R) is nil and R/J(R) is isomorphic to a Boolean ring R1, a Yaqub ring R2, Z5 ...
Huanyin Chen, Marjan Sheibani
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Addendum: A Note on Commutative Nil-Clean Corners in Unital Rings
Известия Иркутского государственного университета: Серия "Математика", 2020 The author wish to add the following to the Acknowledgement section of this Article ”The author would like to express his sincere thanks to Dr. Janez Ster from University of Ljubljana for their joint communication on the subject of the paper and valuable
P.V. Danchev
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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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Amalgamated rings with m-nil clean properties
Ratio Mathematica, 2023 In this paper, we study the transfer of the notion of $m$-nil clean (i.e., a ring in which every element is a sum of a nilpotent and an $m$-potent elements) to the amalgamarted rings.
Vijayanand Venkatachalam +1 more
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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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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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Canadian Mathematical Bulletin, 2009 AbstractA ring R is said to be n-clean if every element can be written as a sum of an idempotent and n units. The class of these rings contains clean rings and n-good rings in which each element is a sum of n units. In this paper, we show that for any ring R, the endomorphism ring of a free R-module of rank at least 2 is 2-clean and that the ring B(R ...
Wang, Zhou, Chen, Jianlong
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