• 제목/요약/키워드: self-cogenerated module

검색결과 2건 처리시간 0.014초

ON THE CHAIN CONDITIONS OF A FAITHFUL ENDO-FLAT MODULE

  • Bae, Soon-Sook
    • 대한수학회논문집
    • /
    • 제14권1호
    • /
    • pp.1-12
    • /
    • 1999
  • The faithful bi-module \ulcornerM\ulcorner with its endomorphism ring End\ulcorner(M) such that M\ulcorner is flat (in other words, End\ulcorner(M)-flat, or endo-flat)and with a commutative ring R containing an identity has been studied in this paper. The chain conditions of a faithful endo-flat module \ulcornerM relative to those of the endomorphism ring End\ulcorner(M) having the zero annihilator of each non-zero endomorphism are studied.

  • PDF

MULTIPLICATION MODULES WHOSE ENDOMORPHISM RINGS ARE INTEGRAL DOMAINS

  • Lee, Sang-Cheol
    • 대한수학회보
    • /
    • 제47권5호
    • /
    • pp.1053-1066
    • /
    • 2010
  • In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring $M^*$ of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of $M^*$ can be found. In particular, two classes of ideals of $M^*$ are discussed in this paper: one is of the form $G_{M^*}\;(M,\;N)\;=\;\{f\;{\in}\;M^*\;|\;f(M)\;{\subseteq}\;N\}$ and the other is of the form $G_{M^*}\;(N,\;0)\;=\;\{f\;{\in}\;M^*\;|\;f(N)\;=\;0\}$ for a submodule N of M.