ZIF环与特征模

ZIF Rings and Character Modules

一个环Ｒ称为左（右）ＺＩＦ环，是指对每一个左（右）Ｒ模Ｍ，Ｍ是内射的当且仅当Ｍ＊是平坦的．Ｒ称为ＺＩＦ环是指它既是左且右的ＺＩＦ环．这里（）＊＝ＨｏｍＺ（－，Ｑ／Ｚ）．本文讨论了ＺＩＦ环的结构以及ＺＩＦ环与其他一些环的关系．

In this paper, ZIF rings are defined. A ring R is called left (right) ZIF ring in case for each left (right) R module M , and M is injective if and only if M is flat. R is called ZIF ring if it is both left and right ZIF. The structure of ZIF rings and some relations between ZIF rings and other rings are discussed. Some characters of the injectinve R modules and their quotient over ZIF ring are obtained.