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Hollow dimension of modules
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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"
}
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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≤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.
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