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
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Journal Article
NS-Primary Submodules
TL;DR: In this article, a proper submodule N of a commutative ring with identity and a unitary R-module M of M is nearly S-primary (for short N S -primary), if whenever,, with ǫ, there exists a positive integer n, such that n is the Jacobson radical of M.
Journal ArticleDOI
Injective property relative to nonsingular exact sequences
TL;DR: In this article, it was shown that the endomorphism ring of an injective R-module has a von Neumann regular factor ring, and that all nonsingular cyclic modules are injective.
Journal ArticleDOI
A Generalization of Semiregular and Almost Principally Injective Rings
A. Çiğdem Özcan,Pınar Aydoğdu +1 more
TL;DR: In this paper, it was shown that a ring R is I-semiregular if and only if for any a ∈ R, there exists a decomposition lRrR(a) = P ⊕ Q, where P = Re ⊆ Ra for some e2 = e ∈ r and Q ∩ r and R = r.
Dissertation
Modules satisfying conditions that are opposites of absolute purity and flatness
TL;DR: In this article, the authors study the properties which are opposites of absolute pure and flat modules, namely, t.f.b.s and subpurity, and show that a right module M is rugged if its flatness domain is the class of all regular right R-modules.
Journal Article
A relative extending module and torsion precovers
M. Kemal Berktas,Semra Dogruoz +1 more
TL;DR: In this paper, the authors characterize -complemented modules with relative (pre)covers and introduce an extending module relative to -pure submodules on a hereditary torsion theory.
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.