具有卷积的弱自反环

Weakly Reflexive Rings with an Involution

基于Chon的可逆环以及Mason提出的自反性概念,研究自反环的相关推广,引入具有卷积的弱自反环(弱*-自反环)的定义,探讨弱*-自反环的性质。得到有关弱*-自反环的4种典型环扩张,如平凡扩张、Dorroh扩张等;推广了相关的经典环扩张的结论,如对于多项式扩张,若R是弱*-自反的拟Armendariz环,则R[x]是弱*^0--自反的。

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 R[x]is weakly*^--reflexive.