Direct sums of CS-modules

A. Harmanci; P. F. Smith; A. Tercan; Y. Tiraş

Direct sums of CS-modules

A. Harmanci
, P. F. Smith
, A. Tercan
, Y. Tiraş

Division of Algebra and Number Theory

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

6 Citations (Scopus)

Abstract

This paper is concerned with when a direct sum of CS-modules is CS. For example, it is proved that for any ring R, the direct sum M = ⊕_i∈IM_i is CS if and only if there exists i ≠ j in I such that every closed submodule K of M with K ∩ M_i = 0 or K ∩ M_j = 0 is a direct summand. In addition, if R is any ring, M₁ a uniform R-module of finite composition length and M₂ a semisimple R-module, then M₁ ⊕ M₂ is CS if and only if M₂ is (M₁/N)-injective for every non-zero submodule N of M₁.

Original language	English
Pages (from-to)	61-71
Number of pages	11
Journal	Houston Journal of Mathematics
Volume	22
Issue number	1
Publication status	Published - 1996

Cite this

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title = "Direct sums of CS-modules",

abstract = "This paper is concerned with when a direct sum of CS-modules is CS. For example, it is proved that for any ring R, the direct sum M = ⊕i∈IMi is CS if and only if there exists i ≠ j in I such that every closed submodule K of M with K ∩ Mi = 0 or K ∩ Mj = 0 is a direct summand. In addition, if R is any ring, M1 a uniform R-module of finite composition length and M2 a semisimple R-module, then M1 ⊕ M2 is CS if and only if M2 is (M1/N)-injective for every non-zero submodule N of M1.",

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year = "1996",

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journal = "Houston Journal of Mathematics",

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T1 - Direct sums of CS-modules

AU - Harmanci, A.

AU - Smith, P. F.

AU - Tercan, A.

AU - Tiraş, Y.

PY - 1996

Y1 - 1996

N2 - This paper is concerned with when a direct sum of CS-modules is CS. For example, it is proved that for any ring R, the direct sum M = ⊕i∈IMi is CS if and only if there exists i ≠ j in I such that every closed submodule K of M with K ∩ Mi = 0 or K ∩ Mj = 0 is a direct summand. In addition, if R is any ring, M1 a uniform R-module of finite composition length and M2 a semisimple R-module, then M1 ⊕ M2 is CS if and only if M2 is (M1/N)-injective for every non-zero submodule N of M1.

AB - This paper is concerned with when a direct sum of CS-modules is CS. For example, it is proved that for any ring R, the direct sum M = ⊕i∈IMi is CS if and only if there exists i ≠ j in I such that every closed submodule K of M with K ∩ Mi = 0 or K ∩ Mj = 0 is a direct summand. In addition, if R is any ring, M1 a uniform R-module of finite composition length and M2 a semisimple R-module, then M1 ⊕ M2 is CS if and only if M2 is (M1/N)-injective for every non-zero submodule N of M1.

UR - https://www.scopus.com/pages/publications/0010126978

M3 - Article

AN - SCOPUS:0010126978

SN - 0362-1588

VL - 22

SP - 61

EP - 71

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 1

ER -

Direct sums of CS-modules

Abstract

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