Journal ArticleDOI
On τ-Extending Modules
Seçil Çeken,Mustafa Alkan +1 more
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TLDR
In this article, a generalization of extending (CS) modules by using the concept of τ-large submodule was introduced, and the authors give some properties of this class of modules and study their relationship with τ-closed, τ-complement submodules and the other generalisation of extending modules (τ-complemented and τ-CS, s−τ-CS modules).Abstract:
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 \(M = \tau (M)\,\oplus\,K\) and K is τ (M)-injective. We also treat when a direct sum of τ-extending modules is τ-extending.read more
Citations
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On the osofsky–smith theorem
TL;DR: In this paper, it was shown that every locally finitely generated Grothendieck category with a family of completely injective generators is a semi-simple ring, where every cyclic module is injective.
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P-Coretractable and Strongly P-Coretractable Modules
TL;DR: Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced.
Journal ArticleDOI
Modules Whose t-Closed Submodules Have a Summand as a Complement
TL;DR: In this paper, the authors define and investigate T 11-type modules as a generalization of t-extending modules, and characterize a module M for which every direct summand satisfies T 11 condition.
Journal ArticleDOI
On pseudo semi-projective modules
TL;DR: In this article, some generalizations of semi-projective modules are studied, namely quasi-pseudo principally projective modules (QPM) and quasi-proximally projective module (PPM).
Journal ArticleDOI
A hyperstructural approach to essentiality
TL;DR: In this paper, the concept of an essential subhypermodule in a hypermodule over a hyperring R such that the intersection of any two subhypermodules of M, is a sub-hypermodule of M is introduced.
References
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Book
Lectures on modules and rings
TL;DR: In this article, Baer's Test for Injectivity is used to evaluate the suitability of a set of Injective Modules over a group of Invertible Fractional Ideals.
Book
An introduction to noncommutative noetherian rings
Ken R. Goodearl,R.B Warfield +1 more
TL;DR: The 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra as mentioned in this paper, and it can be used as a second-year graduate text, or as a self-contained reference.
Journal ArticleDOI
A generalization of CS-modules
TL;DR: In this paper, the authors investigate two generalizations of CS-modules, i.e., if every submodule is essential in a direct sum-mand of a module, and if the module M is a CS-module or satifies (C1).
Journal ArticleDOI
Spectral gabriel topologies and relative singular functors
TL;DR: In this article, Spectral gabriel topologies and relative singular functors are studied in the context of algebraic topologies, and the authors propose a topology based on Spectral Gabbriel topology.