Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MULTIPLICATION MODULES WHOSE ENDOMORPHISM RINGS ARE INTEGRAL DOMAINS

  • Lee, Sang-Cheol (DEPARTMENT OF MATHEMATICS EDUCATION CHONBUK NATIONAL UNIVERSITY, DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF COLORADO AT BOULDER)
  • Received : 2009.04.10
  • Published : 2010.09.30
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Abstract

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.

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References

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