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Abstract. Let R be a ring. We introduce weakly reversible rings, which are a generalization of reversible rings, and investigate their properties. Moreover, we show that a ring R is weakly reversible if and only if for any n, the n-by-n upper triangular matrix ring Tn(R) is weakly reversible. Also some kinds of examples needed in
24 Nov 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. In this note we will study some properties and examples of
10 Oct 2012 generalizations of Armendariz rings, such as McCoy ring, abelian ring and their links. We also consider a skew version of some classes of rings, with respect to a ring endomorphism ?. Keywords: Armendariz ring, skew polynomial ring, reversible, symmetric, semi- commutative ring. MSC: 16S36; 16W20
1 Dec 2003 A ring R is called reversible if ab="0" implies ba="0" for a,b?R. We continue in this paper the study of reversible rings by Cohn [4]. We first consider properties and basic extensions of reversible rings and related concepts to reversible rings, including some kinds of examples needed in the process. We next
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 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.
22 Nov 2017 Full-text (PDF) | 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 {it central reversible} if for any $a$, $bin R$, $ab = 0$ implies $ba$ belongs to the center of $R$. Since every reversible ring is
All our rings will have a unity. A ring R is reversible if, for any a, b ? R, ab = 0 if and only if ba = 0. These rings are natural generalizations of commutative rings. Reversible rings were studied, in particular, by P.M. Cohn [1], Gutan and Kisielewicz [3], Kim and Lee [4] and many others. Our aim, in this short note, is to introduce
27 Mar 2004 For G torsion-free, this is strictly connected with the zero divisor conjecture. In this paper, we characterize reversible rings K[G] for torsion groups. In particular, all finite reversible group rings are described. Our results exhibit a broad class of reversible rings, which are not symmetric. 2004 Elsevier Inc. All
Abstract. We introduce the notion of strongly ?-reversible rings which is a strong version of ?-reversible rings, and investigate its properties. We first give an example to show that strongly reversible rings need not be strongly ?-reversible. We next argue about the strong ?-reversibility of some kinds of extensions. A number of.
matrices. Further, we show in Section 4 that a fully reversible ring is embeddable in a skew field if and only if it is an integral domain. In what follows, all rings are associative, with a unit element 1 which is preserved by ring homomorphisms, inherited by subrings and acts unitally on modules. I am grateful to V. de O. Ferreira

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February 2018