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Reversible Rings with Involutions and Some Minimalities [PDF]
The Scientific World Journal, 2013 In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, *-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative.
W. M. Fakieh, S. K. Nauman
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Journal of Algebra, 2004 An associative ring \(R\) with identity is said to be reversible if \(ab=0\) implies \(ba=0\) for all \(a,b\in R\). The main problem of this paper is the question when the group ring \(K[G]\) of a group \(G\) over a field \(K\) is reversible. The authors prove that if \(G\) is a non-Abelian torsion group and \(K[G]\) is reversible, then \(G\) is ...
Gutan, Marin, Kisielewicz, Andrzej
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A STUDY ON TRI REVERSIBLE RINGS [PDF]
Journal of Algebraic SystemsThis article embodies a ring theoretic property which, preserves the reversibility of elements at non-zero tripotents. A ring R is defined as quasi tri reversible if any non-zero tripotent element ab of R implies ba is also a tripotent element in R for a,
Hussain Mohammed Imdadul Hoque +1 more
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Reversible and symmetric rings
Journal of Pure and Applied Algebra, 2002 A ring is called right (resp. left) duo if every right (resp. left) ideal is two-sided. A ring \(R\) is said to be reversible if \(ab=0\) is equivalent to \(ba=0\) for all \(a,b\in R\). A stronger condition than reversible is symmetric. A ring \(R\) is called symmetric if \(abc=0\) if and only if \(acb=0\) for all \(a,b,c\in R\). In this paper, precise
Greg Marks
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MathematicsThis work explores the notion of axis-reversible rings, a generalization of axis-commutative rings. The objective is to investigate their characteristics and relevance within the wider context of ring theory.
Muhammad Saad, Majed Zailaee
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ON PROPERTIES RELATED TO REVERSIBLE RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2015 We study the connections between idempotents and zero- divisors in several kinds of ring theoretic properties. We next study sev- eral ring theoretic properties and examples related to reversible rings.
, Yang Lee, Sung Ju Ryu
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Taiwanese Journal of Mathematics, 2008 A ring $R$ is called strongly reversible, if whenever polynomials $f(x),$ $g(x)$ in $R[x]$ satisfy $f(x)g(x)=0$, then $g(x)f(x)=0$. It is proved that a ring $R$ is strongly reversible if and only if its polynomial ring $R[x]$ is strongly reversible if and only if its Laurent polynomial ring $R[x,x^{-1}]$ is strongly reversible.
Yang, Gang, Liu, Zhong-Kui
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On duo, reversible and symmetric group rings
Sao Paulo Journal of Mathematical SciencesLet $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications between the ring-theoretic conditions duo, reversible, SI property and symmetric in the setting of group rings.
John H Castillo +2 more
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BAER SPECIAL RINGS AND REVERSIBILITY
Journal of the Chungcheng Mathematical Society, 2014 Abstract. In this paper, we apply some properties of reversiblerings, Baerness of xed rings, skew group rings and Morita Contextrings to get conditions that shows xed rings, skew group ringsand Morita Context rings are reversible. Moreover, we investigateconditions in which Baer rings are reversible and reversible ringsare Baer.
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A Note on Skew Generalized Power Serieswise Reversible Property
International Journal of Analysis and Applications, 2023 The aim of this paper is to introduce and study (S, ω)-nil-reversible rings wherein we call a ring R is (S, ω)-nil-reversible if the left and right annihilators of every nilpotent element of R are equal.
Eltiyeb Ali
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