Weakly Reflexive Rings with an Involution

Based on the reversible rings of Chon and the concept of reflexive by Mason, the related generalization of reflexive rings was studied, the definition of weak reflexive rings with involution was introduced, that is, weakly *- reflexive rings, and the properties of weakly *- reflexive rings were discussed. Four typical ring extensions of weakly *- reflexive rings are obtained, such as trivial extension and Dorroh extension. The conclusions of related classical ring extensions are extended, for polynomial extension, if R be a quasi-Armendariz weakly *- reflexive, then Rx is weakly *- reflexive.