| Hollow dimension of modules |
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| 作者姓名： | ORHAN Nil KESKIN TUTUNCU Derya |
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| 作者单位： | Department of Mathematics，University of Hacettepe，Beytepe 06532，Ankara，Turkey，Department of Mathematics，University of Hacettepe，Beytepe 06532，Ankara，Turkey |
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| 摘 要： | In this paper, we are interested in the following general question: Given a module Mwhich 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 Min terms of hollow dimensions of modules built up in some way from K1 Kn? We prove the following theorem:Let Mbe an amply supplemented module having finite hollow dimension and let Ki (1≤i≤n) be a finite collection of submodules of Msuch that M=K1 ... Kn. Then the hollow dimension h(M) of Mis the sum of the hollow dimensions of Ki (1≤i≤n) ifand only if Ki is a supplement of K1 ... Ki-1 Ki 1 ... Kn in Mfor each 1≤i≤n.
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| 关 键 词： | 补遗子模 空间表达 空间模数 空间分析 |
| 收稿时间： | 2005-01-16 |
| 修稿时间： | 2005-04-21 |
Hollow dimension of modules |
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| ORHAN Nil KESKIN TUTUNCU Derya.Hollow dimension of modules[J].Journal of Zhejiang University Science,2005,6(10):1055-1057. |
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| Authors: | Orhan Nil Keskin Tütüncü Derya |
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| Institution: | (1) Department of Mathematics, University of Hacettepe, Beytepe, 06532 Ankara, Turkey |
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| Abstract: | In this paper, we are interested in the following general question: Given a moduleM which has finite hollow dimension and which has a finite collection of submodulesK i(1≤i≤n) such thatM=K 1+...+Kn, can we find an expression for the hollow dimension ofM in terms of hollow dimensions of modules built up in some way fromK 1, ..., Kn? We prove the following theorem: LetM be an amply supplemented module having finite hollow dimension and letK i(1≤i≤n) be a finite collection of submodules ofM such thatM=K 1+...+Kn. Then the hollow dimensionh(M) ofM is the sum of the hollow dimensions ofK i(1≤i≤n) if and only ifK i is a supplement ofK 1+...+Ki?1+Ki+1+...+Kn inM for each1≤i≤n. |
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| Keywords: | Hollow dimension Supplement submodule |
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