Qnil-对称环及其相关性质研究

Study on Qnil-symmetric Rings and Their Related Properties

本文引进了qnil-对称环的概念,它是对称环的真推广.证明了:二级三角矩阵环(S M0 T)是qnil-对称环当且仅当环S,T都是qnil-对称环;环R上的幂级数环R[[x]]是qnil-对称环当且仅当R是qnil-对称环.

In this paper, we extend symmetric rings and define a new one called qnil-symmetric ring. It is proved that the triangular matrix ring of order two （O^S T^M）is qnil-symmetric if and only if S and T are qnil- symmetric ; the power series ring of R is qnil-symmetric if and only if so is R.