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MULTIPLICATION MODULES WHOSE ENDOMORPHISM RINGS ARE INTEGRAL DOMAINS
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 Title & Authors
MULTIPLICATION MODULES WHOSE ENDOMORPHISM RINGS ARE INTEGRAL DOMAINS
Lee, Sang-Cheol;
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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 of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of can be found. In particular, two classes of ideals of are discussed in this paper: one is of the form $G_{M^*}\;(M,\;N)\;
 Keywords
multiplication module;semi-injective module;self-cogenerated module;tight closed submodule and closed submodule;
 Language
English
 Cited by
 References
1.
S.-S. Bae, On submodules inducing prime ideals of endomorphism ring, East Asian Math. J. 16 (2000), no. 1, 33-48.

2.
S.-S. Bae, Modules with prime endomorphism rings, J. Korean Math. Soc. 38 (2001), no. 5, 987-1030.

3.
C. W. Choi, Multiplication modules and endomorphisms, Math. J. Toyama Univ. 18 (1995), 1-8.

4.
C. W. Choi and P. F. Smith, On endomorphisms of multiplication modules, J. Korean Math. Soc. 31 (1994), no. 1, 89-95.

5.
Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988), no. 4, 755-779. crossref(new window)

6.
E. S. Kim and C. W. Choi, On multiplication modules, Kyungpook Math. J. 32 (1992), no. 1, 97-102.

7.
S. C. Lee, Finitely generated modules, J. Korean Math. Soc. 28 (1991), no. 1, 1-11.

8.
H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1989.

9.
S. Mandal, Projective Modules and Complete Intersections, Springer-Verlag, Berlin, 1997.

10.
E. Mermut, C. Santa-Clara, and P. F. Smith, Injectivity relative to closed submodules, J. Algebra 321 (2009), no. 2, 548-557. crossref(new window)

11.
D. W. Sharpe and P. Vamos, Injective Modules, Cambridge University Press, London-New York, 1972.

12.
W. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505-512. crossref(new window)

13.
S. Wongwai, On the endomorphism ring of a semi-injective module, Acta Math. Univ. Comenian. (N.S.) 71 (2002), no. 1, 27-33.