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Minimal reversible nonsymmetric rings

Affiliation:	1. Institut de Recherche en Mathématique et en Physique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348 Louvain-La-Neuve, Belgium;2. Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742, United States;1. College of Sciences, Shanghai Institute of Technology, 201418 Shanghai, PR China;2. Institut für Algebra und Zahlentheorie, Universität Stuttgart, 70569 Stuttgart, Germany

Abstract:	Marks showed that $F_{2} Q_{8}$ , the $F_{2}$ 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. Furthermore, it is shown that although $F_{2} Q_{8}$ is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo.

Keywords:	Finite rings Reversible rings Symmetric rings Minimal rings 2-Primal rings
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