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RINGS CHARACTERISED BY SEMIPRIMITIVE MODULES
HIRANO, YASUYUKI,IIUYNII, DINII VAN,PARK, JAE KEOL 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.4 No.-
A module M is called a CS-module if every submodule of M is essential in a direct summand of M. It is shown that a ring R is semilocal if and only if every semiprimitive right R-module is CS. Furthermore, it is also shown that the following statements are equivalent for a ring R: (ⅰ) R is semiprimary and every right (or left) R-module is injective; (ⅱ) every countably generated semiprimitive right R-module is a direct sum of a projective module and an injective module.