The Torsion Theory Cogenerated by<i>M</i>-Small Modules

Talebi, Yahya; Vanaja, N.

doi:10.1080/00927870209342390

Cited by 51 publications

(6 citation statements)

References 4 publications

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“…Following [13], a module M is called noncosingular if for every nonzero module N and every nonzero homomorphism f : M → N , Imf is not a small submodule of N . Recall that a ring R is called right hereditary if each of its right ideals is projective.…”

Section: Resultsmentioning

confidence: 99%

Some results on relative dual Baer property

Amouzegar

Tribak

2020

Journal of Algebra Combinatorics Discrete Structures and Applications

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Let R be a ring. In this article, we introduce and study relative dual Baer property. We characterize R-modules M which are RR-dual Baer, where R is a commutative principal ideal domain. It is shown that over a right noetherian right hereditary ring R, an R-module M is N-dual Baer for all R-modules N if and only if M is an injective R-module. It is also shown that for R-modules M1, M2,. . ., Mn such that Mi is Mj-projective for all i > j ∈ {1, 2,. .. , n}, an R-module N is n i=1 Mi-dual Baer if and only if N is Mi-dual Baer for all i ∈ {1, 2,. .. , n}. We prove that an R-module M is dual Baer if and only if S = EndR(M) is a Baer ring and IM = rM (lS(IM)) for every right ideal I of S.

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Section: Resultsmentioning

confidence: 99%

Some results on relative dual Baer property

Amouzegar

Tribak

2020

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…Hence, Z(R) = R . Thus R is cosemisimple by[13, Corollary 2.6]. Since R is commutative, R is von Neumann regular.…”

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confidence: 88%

“…Example 2.2 By applying the last result and some results of [13], we can get some examples of rings having property (P ).…”

Section: Some Properties Of Rings Having ( P )mentioning

confidence: 99%

“…(2) If R is a ring such that every cosingular R -module is projective, then R has property ( P ) by [13,Theorem 3.8(4)].…”

Section: Some Properties Of Rings Having ( P )mentioning

confidence: 99%

“…The module M is said to be small if it is a small submodule of some R -module; equivalently, M is small in its injective hull. In [13], Talebi If for every R -module M , Z(M ) is a direct summand of M , we will say that R has property (P ). The aim of this paper is to shed some light on the structure of rings having (P ).…”

Section: Introductionmentioning

confidence: 99%

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Some rings for which the cosingular submodule of every module is a direct summand

Tütüncü¹,

Ertaş²,

Smith³

et al. 2014

Turk J Math

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The submodule Z(M ) = ∩{N | M/N is small in its injective hull } was introduced by Talebi and Vanaja in 2002. A ring R is said to have propertyshown that a commutative perfect ring R has ( P ) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M ∈ M od − R | ZR(M ) = 0} is closed under factor modules, then R has ( P ) if and only if the ring R is von Neumann regular.

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Modules and Comodules

Brzeziński¹

2008

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The Torsion Theory Cogenerated byM-Small Modules

Cited by 51 publications

References 4 publications

Some results on relative dual Baer property

Some results on relative dual Baer property

Some rings for which the cosingular submodule of every module is a direct summand

Modules and Comodules

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