Results 11 to 20 of about 582,737 (274)

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
doaj   +7 more sources

On Axis-Reversible Rings

Mathematics
This 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
doaj   +5 more sources

Extensions of reversible rings [PDF]

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
exaly   +8 more sources

Reversible and symmetric rings [PDF]

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
Marks, Greg
exaly   +3 more sources

A STUDY ON TRI REVERSIBLE RINGS [PDF]

Journal of Algebraic Systems
This 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, Helen Saikia   +1 more
doaj   +2 more sources

Minimal reversible nonsymmetric rings [PDF]

Journal of Pure and Applied Algebra, 2019
Marks showed that $\mathbb{F}_2Q_8$, the $\mathbb{F}_2$ group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256.
Steve Szabó
exaly   +3 more sources

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., Ungor, B., Halicioglu, S., Harmanci, A.   +3 more
core   +5 more sources

ON STRONGLY REVERSIBLE RINGS

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
exaly   +3 more sources

On duo, reversible and symmetric group rings

Sao Paulo Journal of Mathematical Sciences
Let $RG$ 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, Alexander Holguín-Villa, Brayan Stiven Flórez Burbano   +2 more
exaly   +4 more sources

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.
exaly   +2 more sources