An extension of the reflexive property of rings

Abstract

Mason introduced the notion of reflexive property of rings as a generalization of reduced rings. For a ring endomorphism $\alpha$, Krempa studied $\alpha$-rigid rings as an extension of reduced rings. In this note, we introduce the notion of $\alpha$-quasi reflexive rings as a generalization of $\alpha$-rigid rings and a natural extension of the reflexive property to ring endomorphisms. We investigate various properties of these rings and also study ring theoretic extensions such as polynomial rings, trivial extensions, right (left) quotient rings, Dorroh extensions etc. over these rings.