On some classes of reflexive rings

Abstract

The concept of central reflexive rings is introduced in this paper as a generalization of reflexive rings. Since every reflexive ring is central reflexive, we study the sufficient condition for a central reflexive ring to be a reflexive one. It is shown that every central reversible and hence every central symmetric ring is central reflexive, however converse implications are wrong. It is also proven that the polynomial ring R[x] is central reflexive if R is central reflexive and quasi-Armendariz. We have given some characterizations for an α-reflexive ring and also improved some of the results given by Zhao and Zhu [Extensions of α-reflexive rings, Asian-European J. Math.5(1) (2012) 1–10]. Finally we introduced the concept of central α-reflexive rings as a generalization of α-reflexive rings.