SOME NOTES ON DEDEKIND MODULES

Yıl 2011, Cilt: 40 Sayı: 5, 627 - 634, 01.05.2011

Mehdi Khoramdel Saboura D.p. Hesari

Öz

SOME NOTES ON DEDEKIND MODULES

Öz

In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of O(M)M. In addition it is proved that the endomorphism ring of a finitely generated torsion free Dedekind module M is a Dedekind domain. Also, we give equivalent condition for Dedekind modules, duo modules and uniform modules. Various properties and characterizations of Dedekind modules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.

Anahtar Kelimeler

Dedekind modules and Dedekind domains, Invertible submodules, Duo modules, 2000 AMS Classification: Primary 13 C 10

Kaynakça

• Alkan, M., Sara¸c, B. and Tıra¸s, Y. Dedekind modules, Comm. Alg. 33 (5), 1617–1626, 2005 [2] Anderson, D. D. and Anderson, D. F. Cancellation modules and related modules (Lect. Notes Pure Appl. Math 220, Dekker, New York, 2001), 13-25.
• Azizi, A. Weak multiplication modules, Czech Math. J. 53 (128), 529–534, 2003.
• Bast, Z. E. and Smith, P. F. Multiplication modules, Comm. Alg. 16 (4), 755–779, 1988.
• Kaplansky, I. Commutative Rings (Allyn and Bacon, Boston, 1970).
• Matsumura, H. Commutative Ring Theory (Cambridge University Press, Cambridge, 1989). [7] Naoum, A. G. and Al-Alwan, F. H. Dedekind modules, Comm. Alg. 24 (2), 397–412, 1996. [8] Naoum, A. G. On the ring of endomorphisms of finitely generated multiplication modules, Periodica Mathematica Hungarica 21 (3), 249–255, 1990.
• ¨Ozcan, A. C¸ ., Harmanci. A. and Smith, P. F. Duo modules, Glasgow Math. J. 48, 533–545, 2006. [10] Sara¸c, B., Smith, P. F. and Tıra¸s, Y. On Dedekind modules, Comm. Alg. 35 (5), 1533–1538, 2007. [11] Smith, P. F. Multiplication modules and projective modules, Periodica Mathematica Hun- garica 29 (2), 163–168, 1994.