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Received: 2005-01-16

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.10 P.1055-1057

http://doi.org/10.1631/jzus.2005.A1055


Hollow dimension of modules


Author(s):  ORHAN Nil, KESKİ,N TÜ,TÜ,NCÜ, Derya

Affiliation(s):  Department of Mathematics, University of Hacettepe, Beytepe 06532, Ankara, Turkey

Corresponding email(s):   nilorhan@hacettepe.edu.tr, keskin@hacettepe.edu.tr

Key Words:  Hollow dimension, Supplement submodule


ORHAN Nil, KESKİN TÜTÜNCÜ Derya. Hollow dimension of modules[J]. Journal of Zhejiang University Science A, 2005, 6(10): 1055-1057.

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Abstract: 
In this paper, we are interested in the following general question: Given a module M which has finite hollow dimension and which has a finite collection of submodules Ki (1≤in) such that M=K1+...+Kn, can we find an expression for the hollow dimension of M in terms of hollow dimensions of modules built up in some way from K1,...,Kn We prove the following theorem: Let M be an amply supplemented module having finite hollow dimension and let Ki (1≤in) be a finite collection of submodules of M such that M=K1+...+Kn. Then the hollow dimension h(M) of M is the sum of the hollow dimensions of Ki (1≤in) if and only if Ki is a supplement of K1+...+Ki−1+Ki+1+...+Kn in M for each 1≤in.

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Reference

[1] Grezeszcuk, P., Puczylowski, E.R., 1984. On Goldie and dual Goldie dimension. J. Pure App. Algebra, 31:47-54.

[2] Hanna, A., Shamsuddin, A., 1984. Duality in the Category of Modules. Applications, Algebra Berichte 49, Verlag Reinhard Fischer München.

[3] Keskin, D., 2000. On lifting modules. Comm. Alg., 28:3427-3440.

[4] Lomp, C., 1996. On Dual Goldie Dimension. Diplomarbeit (M.Sc. Thesis), HHU Düsseldorf, Germany.

[5] Miyashita, Y., 1966. Quasi-projective modules, perfect modules and a theorem for modular lattices. J. Fac. Sci. Hokkaido, 19:86-110.

[6] Mohamed, S.H., Müller, B.J., 1990. Continuous and Discrete Modules. London Math. Soc. Lecture Notes Series, 147, Cambridge.

[7] Rim, S.H., Takemori, K., 1993. On dual Goldie dimension. Comm. Alg., 21:665-674.

[8] Wisbauer, R., 1991. Foundations of Module and Ring Theory. Gordon and Breach, Philadelphia.

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