• 제목/요약/키워드: maximal open submodule

검색결과 2건 처리시간 0.014초

OPENLY SEMIPRIMITIVE PROJECTIVE MODULE

  • Bae, Soon-Sook
    • 대한수학회논문집
    • /
    • 제19권4호
    • /
    • pp.619-637
    • /
    • 2004
  • 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.