Generalizations of CS-modules

Smith, Patrick F.; Tercan, Adnan

doi:10.1080/00927879308824655

Cited by 71 publications

(38 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let N be a direct summand of M . Then N is also a direct sum of uniform modules by [15,Theorem 5.5]. Now Corollary 2.9 yields that N is also self-p-injective.…”

Section: Direct Summands and Direct Sumsmentioning

confidence: 94%

Modules which are self-p-injective relative to projection invariant submodules

Kara

Tercan

2017

Analele Universitatii "Ovidius" Constanta - Seria Matematica

View full text Add to dashboard Cite

show abstract

“…Let N be a direct summand of M . Then N is also a direct sum of uniform modules by [15,Theorem 5.5]. Now Corollary 2.9 yields that N is also self-p-injective.…”

Section: Direct Summands and Direct Sumsmentioning

confidence: 94%

Modules which are self-p-injective relative to projection invariant submodules

Kara

Tercan

2017

Analele Universitatii "Ovidius" Constanta - Seria Matematica

View full text Add to dashboard Cite

show abstract

“…Rings for which a certain class of modules satisfies some "generalized extending property" have been studied by many authors (see [5], [15], [16]). In recent years, torsion-theoretic analogues of extending (CS) modules have been attracting some authors' attention: Smith, De Viola-Prioli, Viola-Prioli, Charalambides, Clark and Dogruöz. In 1997, ( [17]), Smith, De Viola-Prioli and E. Viola-Prioli defined τ -complemented modules, which is that a module M is said to be τ -complemented if every submodule of M is τ -dense in a direct summand of M where τ is a torsion theory on Mod-R.…”

Section: Introductionmentioning

confidence: 99%

On τ-Extending Modules

Çeken

Alkan

2010

Mediterr. J. Math.

View full text Add to dashboard Cite

Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of τ -large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with the familiar concepts of τ -closed, τ -complement submodules and the other generalization of extending modules (τ -complemented, τ -CS, s-τ -CS modules). We are also interested in determining when a τ -divisible module is τ -extending. For a τ -extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that M = τ (M ) ⊕ K and K is τ (M )-injective. We also treat when a direct sum of τ -extending modules is τ -extending.Mathematics Subject Classification (2010). Primary 16S90; Secondary 16D50, 16D70.

show abstract

“…The motivation for the study of these properties was provided by the following result of Kaplansky [5]: a free module over a principal ideal domain, PID, has SIP. This property has been studied by many authors including [1], [3], [4] and [9].Recall that a module M is called a C 11 -module (or satisfies C 11 ) if every submodule of M has a complement which is a direct summand (see [7], [8]). Following [7], a module is called a C + 11 -module if every direct summand of the module is a C 11 -module.…”

mentioning

confidence: 98%

When is the SIP (SSP) property inherited by free modules

2006

View full text Add to dashboard Cite

A right R-module M has right SIP (SSP) if the intersection (sum) of two direct summands of M is also a direct summand. It is shown that the right SIP (SSP) is not a Morita invariant property and that a nonsingular C + 11 -module does not necessarily have SIP. In contrast, it is shown that the direct sum of two copies of a right Ore domain has SIP as a right module over itself.Throughout this paper all rings are associative with unity and R always denotes such a ring. Modules are unital and for an abelian group M , we use M R (resp. R M ) to denote a right (resp. left) R-module.A module M R has the summand intersection (resp. sum) property, SIP (resp. SSP), if the intersection (resp. sum) of every pair of direct summands of M R is a direct summand of M R . The motivation for the study of these properties was provided by the following result of Kaplansky [5]: a free module over a principal ideal domain, PID, has SIP. This property has been studied by many authors including [1], [3], [4] and [9].Recall that a module M is called a C 11 -module (or satisfies C 11 ) if every submodule of M has a complement which is a direct summand (see [7], [8]). Following [7], a module is called a C + 11 -module if every direct summand of the module is a C 11 -module.

show abstract

Generalizations of CS-modules

Cited by 71 publications

References 6 publications

Modules which are self-p-injective relative to projection invariant submodules

Modules which are self-p-injective relative to projection invariant submodules

On τ-Extending Modules

When is the SIP (SSP) property inherited by free modules

Contact Info

Product

Resources

About