Hollow dimension of modules

Nil Orhan; Tutuncu Derya Keskïn

doi:10.1631/jzus.2005.A1055

Hollow dimension of modules

Nil Orhan
, Tutuncu Derya Keskïn

Division of Algebra and Number Theory

Hacettepe University

Research output: Contribution to journal › Article › peer-review

Abstract

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 K_i(1 ≤ i ≤ n) such that M = K₁ + ⋯ + K_n, 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, ⋯, K_n? We prove the following theorem: Let M be an amply supplemented module having finite hollow dimension and let K_i(1 ≤ i ≤ n) be a finite collection of submodules of M such that M = K₁+ ⋯ + K_n. Then the hollow dimension h(M) of M is the sum of the hollow dimensions of K_i (1 ≤ i ≤ n) if and only if K_i is a supplement of K₁ + ⋯ + K_i-1 + K_i+1 + ⋯ + K_n in M for each 1 ≤ i ≤ n.

Original language	English
Pages (from-to)	1055-1057
Number of pages	3
Journal	Journal of Zhejinag University: Science
Volume	6 A
Issue number	10
DOIs	https://doi.org/10.1631/jzus.2005.A1055
Publication status	Published - Oct 2005

Keywords

Hollow dimension
Supplement submodule

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10.1631/jzus.2005.A1055

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title = "Hollow dimension of modules",

abstract = "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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language = "English",

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T1 - Hollow dimension of modules

AU - Orhan, Nil

AU - Keskïn, Tutuncu Derya

PY - 2005/10

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AB - 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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KW - Supplement submodule

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DO - 10.1631/jzus.2005.A1055

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SP - 1055

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JO - Journal of Zhejinag University: Science

JF - Journal of Zhejinag University: Science

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ER -

Hollow dimension of modules

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