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

Cebir ve Sayılar Teorisi Anabilim Dalı

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

6 Alıntılar (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	61-71
Sayfa sayısı	11
Dergi	Houston Journal of Mathematics
Hacim	22
Basın numarası	1
Yayın durumu	Yayınlandı - 1996

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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.",

author = "A. Harmanci and Smith, \{P. F.\} and A. Tercan and Y. Tira{\c s}",

year = "1996",

language = "English",

volume = "22",

pages = "61--71",

journal = "Houston Journal of Mathematics",

issn = "0362-1588",

publisher = "University of Houston",

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TY - JOUR

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

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