关于弱遗传环与弱半单环

On weak hereditary rings and weak semisimple rings

引入弱投射模,得到弱投射模类的等价刻画和若干封闭性,证明了弱投射模类为投射可解类;引入并刻画两类新的环即弱半单环和弱遗传环,证明了弱投射模与弱内射模、弱半单环与弱余半单环、弱遗传环与弱余遗传环分别构成了Morita对偶对.

In this paper, we introduce the concept of weak projective modules, obtain equivalent characterizations and some closeness of weak projective modules, and prove that the class of weak projective modules is resolving. We also introduce and characterize two new classes of rings,i.e.,weak semisimple rings and weak hereditary rings. We prove that weak projective modules and weak injective modules, weak semisimple rings and weak cosemisimple rings,weak hereditary rings and weak cohereditary rings constitute Morita dual pairs respectively.