| The strongly prime submodules play important roles in the study of rings andcategories of modules. Some properties of strongly prime submodules are studied,it is shown that if ?? is a submodule of M,L is a strongly prime submodule ofM such that N (?)L. Then (L∩N : N) = (L: M) and L∩N is a strongly primesubmodule of N. The de?nitions of S-isolated submodules and S-prime radicalsubmodules are given through strongly prime submodules in this paper. It is shownthat if M =M1⊕M2 is a duo module and N1, N2 are S-isolated submodulesof M1, M2, respectively, then N1⊕N2 is an S-isolated submodule of M.
|
PDF Full Text Request