MULTIPLICATION MODULES WHOSE ENDOMORPHISM RINGS ARE INTEGRAL DOMAINS
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In this paper, several properties of endomorphism rings of modules are investigated. A multiplication moduleM over a commutative ring R induces a commutative ring M* of endomorphisms of M and hence the relation between the prime (maximal) submodules ofM 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 GM* (M,N) ={f ∈ M* | f(M) ⊆ N} and the other is of the form GM* (N, 0) = {f ∈M* | f(N) = 0} for a submodule N of M.
Abstract
In this paper, several properties of endomorphism rings of modules are investigated. A multiplication moduleM over a commutative ring R induces a commutative ring M* of endomorphisms of M and hence the relation between the prime (maximal) submodules ofM 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 GM* (M,N) ={f ∈ M* | f(M) ⊆ N} and the other is of the form GM* (N, 0) = {f ∈M* | f(N) = 0} for a submodule N of M.
참고문헌 (13)
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