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Left orders in strongly regular rings
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1993 SynopsisIn 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 Note on Strongly π-Regular Rings
Acta Mathematica Hungarica, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Almost Strongly Regular Rings
Journal of Algebra and Its ApplicationsA ring [Formula: see text] is called almost strongly regular if for each [Formula: see text] either [Formula: see text] or [Formula: see text] is strongly regular. The class of almost strongly regular rings lies properly between the class of strongly regular rings and the class of strongly clean rings.
Yuanlin Li, Jian Cui
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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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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 ).
B. Sambathkumar +2 more
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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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Journal of Algebra and Its Applications, 2019
Let [Formula: see text] be a ring with involution ∗. An element [Formula: see text] is called ∗-strongly regular if there exists a projection [Formula: see text] of [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text] is invertible, and [Formula: see text] is said to be ∗-strongly regular if every element of ...
Long Wang, Yinchun Qu, Junchao Wei
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Let [Formula: see text] be a ring with involution ∗. An element [Formula: see text] is called ∗-strongly regular if there exists a projection [Formula: see text] of [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text] is invertible, and [Formula: see text] is said to be ∗-strongly regular if every element of ...
Long Wang, Yinchun Qu, Junchao Wei
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A note on strongly regular near-rings
Publicationes Mathematicae Debrecen, 2022In this interesting short note, the authors prove that if N is a strongly regular near-ring, then the maximum condition on ideals implies the minimum condition on ideals. In ring theory, it is well known that if every nilpotent element is in the center then every idempotent is central. Hence a regular ring without nilpotent element is strongly regular.
Reddy, Y. V., Murty, C. V. L. N.
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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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On strongly \(\pi\)-regular rings and periodic rings
Mathematical Journal of Okayama University, 1985A 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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