P—CS模的遗传性

每个循环子模都是其直和项的本质子模的模称为P—CS模，它是CS-模的推广．模M满足C2条件是指若M的子模N同构于M的直和项，则N是M的直和项．模M满足C3条件是指若M1，M2是M的直和项且M1∩M2=0，则M1＋M2是M的直和项．证明了满足C2或C3条件的P—CS模对其直和保持遗传性．进一步讨论了P-CS模对一般子模的遗传性问题，利用内射包，给出了P—CS模对一般子模保持遗传性的一些等价刻画．

Hereditary properties of P-CS modules

The class of P-CS modules was an extension of CS modules,in which every cyclic submodule of Mwas essential in its direct summand.M was called satisfied the condition C2 if the submodule N was isomorphicto a direct summand of M,where N was a direct summand of M.M was called satisfied the condition C3 if M1,M2 were direct summands of M,M1∩M2 = 0,then M1M2 was a direct summand of M.It was investigatedthe equivalence of the P-CS property between a module and its direct summand.The conditions under whichthe submodules of a P-CS module were also P-CS modules were discussed as well.Then the injective hull ofmodule was utilized to determine the P-CS condition for modules.