CLC number: O177
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 0
Clicked: 6099
ORHAN Nil, KESKİN TÜTÜNCÜ Derya. Hollow dimension of modules[J]. Journal of Zhejiang University Science A, 2005, 6(10): 1055-1057.
@article{title="Hollow dimension of modules",
author="ORHAN Nil, KESKİN TÜTÜNCÜ Derya",
journal="Journal of Zhejiang University Science A",
volume="6",
number="10",
pages="1055-1057",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A1055"
}
%0 Journal Article
%T Hollow dimension of modules
%A ORHAN Nil
%A KESKİ
%A N TÜ
%A TÜ
%A NCÜ
%A Derya
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 10
%P 1055-1057
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A1055
TY - JOUR
T1 - Hollow dimension of modules
A1 - ORHAN Nil
A1 - KESKİ
A1 - N TÜ
A1 - TÜ
A1 - NCÜ
A1 - Derya
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 10
SP - 1055
EP - 1057
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A1055
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≤i≤n) 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≤i≤n) 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≤i≤n) if and only if Ki is a supplement of K1+...+Ki−1+Ki+1+...+Kn in M for each 1≤i≤n.
[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.
Open peer comments: Debate/Discuss/Question/Opinion
<1>