广义幂级数环上Morita Context环的稳定条件

Stable Rings for Morita Contexts of Generalized Power Series Rings

中文关键词:  Context  单位1-正则  广义幂级数.

英文关键词:Morita Context  unit 1-stable range  generalized power series.

中文摘要:

      本文证明了如果环$A, B$分别是$(S,2)-$环,单位1-正则环或 $GM-$环,那么广义幂级数环上的Morita Context环 $([[A^{S,\leq}]], [[B^{S,\leq}]],[[M^{S,\leq}]],[[N^{S,\leq}]],\psi^{S},\phi^{S})$也分别是$(S,2)-$环,单位1-正则环或 $GM-$环.于是我们得到了一类新的满足稳定条件的环类.

英文摘要:

      In this paper, we show that if rings $A$ and $B$ are $(s,2)$-rings, then so is the ring of a Morita Context $([[A^{S,\leq}]], [[B^{S,\leq}]],[[M^{S,\leq}]],[[N^{S,\leq}]],\psi^{S},\phi^{S})$ of generalized power series. Also we get analogous results for unit 1-stable ranges, $GM$-rings and rings which have stable range one. These give new classes of rings satisfying such stable range conditions.