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On Strongly ?-Regular Group Rings
Southeast Asian Bulletin of Mathematics, 2003An element \(x\) in a ring \(R\) is said to be left or right \(\pi\)-regular if there exists \(y\in R\) and a positive integer \(n\) such that \(x^n=yx^{n+1}\) or \(x^n=x^{n+1}y\), respectively. If \(x\) is both left and right \(\pi\)-regular, then it is strongly \(\pi\)-regular, and \(R\) is said to be a strongly \(\pi\)-regular ring if all its ...
Chin, A. Y. M., Chen, H. V.
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Acta Mathematica Hungarica, 1990
An associative ring \(R\) with identity is called strongly regular if for each \(a\in R\) there is an \(x\in R\) such that \(a=a^ 2x\). It is easy to see that a Noetherian ring \(R\) is strongly regular if and only if it is a finite direct product of division rings.
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An associative ring \(R\) with identity is called strongly regular if for each \(a\in R\) there is an \(x\in R\) such that \(a=a^ 2x\). It is easy to see that a Noetherian ring \(R\) is strongly regular if and only if it is a finite direct product of division rings.
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Left orders in strongly regular rings
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1993SynopsisIn this paper we characterise left orders in strongly regular rings, both for classical left orders and left orders in the sense of Fountain and Gould [2] where the ring of quotients need not have an identity.
Ánh, Pham Ngoc, Márki, László
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A type of strongly regular rings
Journal of Intelligent & Fuzzy Systems, 2015In this study, using Yuan and Lee’s definition of fuzzy group based on fuzzy binary operation and Aktas and Cagman definition of fuzzy ring, we give a new kind of definition to ( A : B ). The concept of fuzzy regular and fuzzy left strongly regular are introduced and we create a new study ...
Sambathkumar, B. +2 more
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A note on strongly π-regular rings
Acta Mathematica Hungarica, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A generalization of strongly regular rings
Acta Mathematica Hungarica, 1984A ring \(A\) is s-weakly regular if for all \(a\) in \(A\) \(a\) is in \(aAa^ 2A\). The class of s-weakly regular rings lies strictly between the class of strongly regular rings and the class of weakly regular rings. Just as strongly regular rings are the reduced regular rings, the s-weakly regular rings are the reduced weakly regular rings. A ring \(A\
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On Strongly -Regular Rings and Strongly Commuting -Regular Rings
Journal of Garmian University, 2017Abdullah Abdul-Jabbar, Lavan Mustafa
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On strongly \(\pi\)-regular rings and periodic rings
2016A ring R is called normal if every idempotent is central. Let \(P=\{x\in R:\) \(xe=x\) for some idempotent e and \(xy=0\) iff \(ey=0\) for \(y\in R\}\). An element \(x\in R\) is called strongly regular if for some y in R \(x=x^ 2y=yx^ 2\). It is called regular if \(xyx=x\) for some y. It is called \(\pi\)-regular (resp. strongly \(\pi\)-regular) if \(x^
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Strongly Additively Regular Rings and Graphs
2019A commutative ring R is said to be additively regular if for each pair of elements \(f,g\in R\) with f regular, there is an element \(t\in R\) such that \(g+ft\) is regular. For any commutative ring R, the polynomial ring \(R[{\scriptstyle \mathrm {X}}]\) is additively regular, moreover if \(deg(g)
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Some generalizations of strongly regular rings. III
1972A ring A is called a P1-ring if aAa = aA for all a 2 A. The author's main results are the following theorems. Theorem 6: For an arbitrary ring A with no nonzero nilpotent ideals the following two conditions are equivalent: (i) A is a P1 ring, (ii) A is strongly regular (i.e., a 2 a2A for any a 2 A).
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