α-Reflexive Rings with Involution

Abstract

This paper studies the concept of the -quasi-*-IFP (resp.,  -*-reflexive) *-rings, as a generalization of the quasi-*-IFP (resp., *-reflexive) *-rings and every quasi-*-IFP (resp., *-reflexive) *-ring is  -quasi-*-IFP (resp., -*-reflexive). This paper also discusses the sufficient condition for the quasi-*-IFP (resp., *-reflexive) *-ring in order to be -quasi-*-IFP (resp., -*- reflexive). Finally, this study investigates the -quasi-*-IFP (resp., -*-reflexivity) by using some types of the polynomial rings.