Results 1 to 10 of about 1,006,297 (273)
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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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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RING ENDOMORPHISMS WITH THE REVERSIBLE CONDITION [PDF]
Communications of the Korean Mathematical Society, 2010 P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a,b 2 R. Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and fi an endomorphism of R, we say that R is right (resp., left) fi-shifting if whenever afi(b) = 0 (resp., fi(a)b = 0) for a,b 2 ...
Fatma Kaynarca, Muhittin Baser
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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 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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On GP-InjectivityWith Some Types of Rings [PDF]
مجلة التربية والعلم, 2007 The purpose of this paper is to study GP-injective modules and give some of it is properties. Also, we proved: (1) If every simple right R-module is GP-injective, and R is reversible ring, then R is a right weakly -regular.
Abdullah M. Abdul-Jabbar +1 more
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Extensions of reversible rings
Journal of Pure and Applied Algebra, 2003 A ring \(R\) is called reversible if \(ab = 0\) implies \(ba = 0\) for \(a,b\) \(\in R\). Some authors call this ring zero-commutative. The authors obtain some basic properties of basic extensions of these rings. Let \(T(R,R)\) and \(R[x]\) be the \(2\) by \(2\) upper triangular matrix ring and polynomial ring over \(R\), respectively.
Kim, Nam Kyun, Lee, Yang
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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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Extensions of i-reversible rings
Journal of Algebra and Its Applications, 2023 A ring [Formula: see text] is said to be i-reversible if for every [Formula: see text] [Formula: see text][Formula: see text], [Formula: see text] is a nonzero idempotent implies [Formula: see text] is an idempotent. It is known that the rings [Formula: see text] and [Formula: see text] (the ring of all upper triangular matrices over [Formula: see ...
Lama, Vivek Bhabani +3 more
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