Abstract

In this paper, a left module over an associative ring with identity is defined to be openly semiprimitive (strongly semiprimitive, respectively) by the zero intersection of all maximal open fully invariant submodules (all maximal open submodules which are fully invariant, respectively) of it. For any projective module, the openly semiprimitivity of the projective module is an equivalent condition of the semiprimitivity of endomorphism ring of the projective module and the strongly semiprimitivity of the projective module is an equivalent condition of the endomorphism ring of the projective module being a sub direct product of a set of subdivisions of division rings.

주제어

#free   #projective   #semiprimitive   #openly (strongly) semi-primitive module   #maximal open submodule   #prime endomorphism  

참고문헌 (10)

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이 논문을 인용한 문헌 (1)

1. 2008. "" Honam mathematical journal = 호남수학학술지, 30(4): 617~629  원문보기 상세보기