广义D4模

Generalized D4 modules

作为D4模的真推广,引入了广义D4模的概念.研究了这类模的基本性质,给出了广义D4模的一些等价条件.进一步引入了拟D4模的概念,证明了环R是半单环当且仅当每个R-模是拟D4模.

As a proper generalization of D4 modules, the concept of generalized D4 modules is introduced in this paper. Some equivalent conditions of generalized D4 modules are given by studing the basic proerties of such modules. Furthermore, the concept of pseudo D4 modules is introduced. and it is shown that a ring R is semisimple if and only if each R-module is a pseudo D4 module.