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Reversible ring property via idempotent elements
Georgian Mathematical Journal, 2022 Regarding the question of how idempotent elements affect the reversible property of rings, we study a version of reversibility depending on idempotents. In this perspective, we introduce right (resp., left) e-reversible rings.
Handan Kose +2 more
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On weakly reversible rings and strongly reversible rings
Publicationes Mathematicae Debrecen, 2010The authors introduce the following class of rings which contains all commutative and all reduced rings: a ring \(R\) is called weakly reversible if \(ab=0\) implies the existence of \(x,y,z\in R\) such that \(xbyaz\) is a nilpotent element. In the paper the behaviour of weakly reversible rings under diverse constructions is studied.
Zhao, Liang, Zhu, Xiaosheng
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Journal of Algebra and Its Applications, 2019
We study rings in which [Formula: see text] nonzero idempotent implies [Formula: see text] is also an idempotent. We call such rings i-reversible. Besides studying the basic properties of i-reversible rings, we characterize i-reversible triangular matrix rings, i-reversible matrix rings over commutative rings and i-reversible exchange rings.
Khurana, Anjana, Khurana, Dinesh
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We study rings in which [Formula: see text] nonzero idempotent implies [Formula: see text] is also an idempotent. We call such rings i-reversible. Besides studying the basic properties of i-reversible rings, we characterize i-reversible triangular matrix rings, i-reversible matrix rings over commutative rings and i-reversible exchange rings.
Khurana, Anjana, Khurana, Dinesh
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Reversibility of tubal ring sterilization
Contraception, 1977Abstract The reversibility of the tubal ring sterilization technique was studied in 22 rabbits. Using microsurgery for end-to-end reanastomosis, a patency rate of 96% and a pregnancy rate of 86% was obtained. It is suggested that human tubal ring sterilization has a high probability of being reversible, although several factors of reversibility ...
W D, Boeckx, G, Vasquez, I A, Brosens
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Reverse mathematics and semisimple rings
Archive for Mathematical Logic, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalizations of reversible and Armendariz rings
International Journal of Algebra and Computation, 2016This paper concerns several ring theoretic properties related to matrices and polynomials. The basic properties of [Formula: see text]-reversible and power-Armendariz are studied. We provide a method by which one can always construct a power-Armendariz ring but neither symmetric nor Armendariz from given any symmetric ring. We investigate next various
Juncheol Han +4 more
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Bulletin of the London Mathematical Society, 1999
A ring \(R\) is called reversible if \(ab=0\) implies \(ba=0\); it is insertable if \(ab=0\) implies \(aRb=0\). Clearly any reversible ring is insertable, but not conversely. The author proves that a ring is (i) an integral domain if and only if it is prime and reversible (insertable), (ii) reduced if and only if it is semiprime and reversible ...
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A ring \(R\) is called reversible if \(ab=0\) implies \(ba=0\); it is insertable if \(ab=0\) implies \(aRb=0\). Clearly any reversible ring is insertable, but not conversely. The author proves that a ring is (i) an integral domain if and only if it is prime and reversible (insertable), (ii) reduced if and only if it is semiprime and reversible ...
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e-reversibility of rings via quasinilpotents
Georgian Mathematical Journal, 2023Abstract The reversible property of rings was introduced by Cohn and has important generalizations in noncommutative ring theory. In this paper, reversibility of rings is investigated in relation with quasinilpotents and idempotents, and our argument is spread out based on this. We call a ring R Qnil e-reversible if for
Handan Kose +2 more
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On a property of polynomial rings over reversible rings
Communications in Algebra, 2018In this article, we first observe a sort of property of ideals generated by zero-dividing polynomials over reversible rings, in relation with products of ideals at zero.
Hai-lan Jin +4 more
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Reversibility in matrix rings and group algebras
Periodica Mathematica HungaricazbMATH Open Web Interface contents unavailable due to conflicting licenses.
Truong Huu Dung +2 more
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