具有卷积的中心自反环

Central Reflexive Rings with an Involution

中文关键词:  -自反环  中心-自反环  中心-半交换环  Dorroh扩张

英文关键词:$*$-reflexive rings  central $*$-reflexive rings  central $\ast$-semicommutative ring  Dorroh extension

中文摘要:

      本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.

英文摘要:

      We study the central reflexive properties of rings with an involution. The concept of central $*$-reflexive rings is introduced and investigated. It is shown that central $*$-reflexive rings are a generalization of reflexive rings, central reflexive rings and $\ast$-reflexive rings. Some characterizations of this class of rings are given. The related ring extensions including trivial extension, Dorroh extension and polynomial extensions are also studied.