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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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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 ...
Muhittin Baser, Fatma Kaynarca
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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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Conformation-driven reversibility control in ring-opening metathesis polymerization of non-bicyclic cyclooctenes [PDF]
Nature CommunicationsReversible ring-opening metathesis polymerization (ROMP) of cyclooctene (COE) derivatives remains a challenge due to their high ring strain energies (RSEs).
Trimbak Baliram Mete +7 more
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On Double Cyclic Codes over Finite Chain Rings for DNA Computing [PDF]
EntropyLet e be a fixed positive integer and n1,n2 be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length (n1,n2) over the finite chain ring Re = F4e+vF4e, where v2=0.
Shakir Ali +4 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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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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Lewis Acid‐Triggered Spatiotemporally Controllable Ring Opening in a Classic Rhodamine Featuring Φ = 95% Emission [PDF]
Small ScienceRhodamine derivatives, as a prominent class of fluorophores, have become indispensable in advanced material engineering and biomedical research due to their exceptional photostability and tunable optical characteristics.
Quanchun Sun +4 more
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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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