矩阵Γ_(n,m)—环M_(m,n)的F—正则性

F-regularity for Matrix F_(n,m)-ring M_(m,n)

讨论Γ—环M上的矩阵Γ_(n,m)—环M_(m.n)的F—正则性。得出Γ_(n.m)—环M_(m.n)的理想Q为F—正则理想的充要条件是在Γ—环M中存在F—正则理想P使得Q=P_(m,n)。

In this paper, we discuss the F-regularity for the matrix г_(n,m)-ring M_(m,n) over г-ring M. We obtain mainlythe following result: the ideal Q of г_(n,m)-ring M_(m,n) is an F-regular ideal if and only if there is an F-regular ideal P, in theг-ring M such that Q=P_(m,n).