Clean环及其扩张

Clean Rings and their Extensions

讨论了clean环的几个重要性质,证明了R是clean环当且仅当R上的可数(有限或列有限)的上三角矩阵环是clean环,也当且仅当R上的可数(有限或行有限)的下三角矩阵环是clean环,在一定条件下证明了clean环是Morita不变量。

Some properties of clean rings are discussed. It is shown that R is a clean ring if and only if every countable upper triangular matrix ring （finite or column finite） is a clean ring. In addition, under certain conditions, it is proved that clean ring is Morita invariant.