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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 generalization of reversible rings [PDF]
, 2014 In this paper, we introduce a class of rings which is a generalization of reversible rings. Let R be a ring with identity. A ring R is called central reversible if for any a,b א R, ab=0 implies ba belongs to the center of R. Since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible ...
Kose, H. +3 more
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Reversibility of Rings with Respect to the Jacobson Radical [PDF]
Mediterranean Journal of Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Calci, Mete Burak +3 more
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Algebra Colloquium, 2009 An endomorphism α of a ring R is called right reversible if whenever ab = 0 for a, b ∈ R, then bα(a) = 0. A ring R is called right α-reversible if there exists a right reversible endomorphism α of R. The notion of an α-reversible ring is a generalization of α-rigid rings as well as an extension of reversible rings.
Baser, Muhittin +2 more
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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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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 $\mathcal Z$-reflexive rings [PDF]
Mathematica BohemicaWe introduce the notion of $\mathcal Z$-reflexive rings to describe reflexivity of rings in terms of their singular ideals. We show that $\mathcal Z$-reflexive ring is proper common generalization of a central reflexive ring, $\mathcal Z$-reversible ring,
Nirbhay Kumar
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Ore extensions of zip and reversible rings
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2006 Bu makalede zip ve reversible halkaların Ore genişlemeleri çalışılmıştır. R bir halka, $\\alpha$; R nin bir endomorfizması ve $\\delta$ bir $\\alpha$-türev olmak üzere; aşağıdakiler ispatlanmıştır. (1) R nin bir sağ zip halka olması için gerek ve yeter koşul R[x; $\\alpha$, $\\delta$ ] nın bir sağ zip halka olmasıdır.
Baser, Muhittin
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On Reversible Group Rings [PDF]
Bulletin of the Australian Mathematical Society, 2006 Let G be an arbitrary finite group, R be a finite associative ring with identity and RG be the group ring. We show that ℤ2Q8 is the minimal reversible group ring which is not symmetric, and we also characterise the finite rings R for which RQ8 is reversible. The first result extends a result of Gutan and Kisielewicz which shows that ℤ2Q8 is the minimal
Li, Yuanlin +2 more
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