scholarly journals Pure Baer injective modules

1997 ◽  
Vol 20 (3) ◽  
pp. 529-538 ◽  
Author(s):  
Nada M. Al Thani
Keyword(s):  
Essential Extension ◽  
Injective Module ◽  
Algebraic Structures ◽  
Basic Properties ◽  
Injective Modules ◽  
Relative Complement

In this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of a∑-pure Baer injective module and that of SSBI-ring. A ringRis an SSBI-ring if and only if every smisimpleR-module is pure Baer injective. To investigate such algebraic structures we had to define what we callp-essential extension modules, pure relative complement submodules, left pure hereditary rings and some other related notions. The basic properties of these concepts and their interrelationships are explored, and are further related to the notions of pure split modules.

Quasi-pseudo Principally Injective Modules

2009 ◽  
Vol 16 (03) ◽  
pp. 397-402 ◽  
Author(s):  
Avanish Kumar Chaturvedi ◽  
B. M. Pandeya ◽  
A. J. Gupta
Keyword(s):  
Injective Module ◽  
Injective Modules

In this paper, the concept of quasi-pseudo principally injective modules is introduced and a characterization of commutative semi-simple rings is given in terms of quasi-pseudo principally injective modules. An example of pseudo M-p-injective module which is not M-pseudo injective is given.

ON M-C-INJECTIVE AND SELF-C-INJECTIVE MODULES

2010 ◽  
Vol 03 (03) ◽  
pp. 387-393 ◽  
Author(s):  
A. K. Chaturvedi ◽  
B. M. Pandeya ◽  
A. M. Tripathi ◽  
O. P. Mishra
Keyword(s):  
Endomorphism Ring ◽  
Projective Module ◽  
Injective Module ◽  
Injective Modules ◽  
Factor Module ◽  
Closed Submodule

Let M1 and M2 be two R-modules. Then M2 is called M1-c-injective if every homomorphism α from K to M2, where K is a closed submodule of M1, can be extended to a homomorphism β from M1 to M2. An R-module M is called self-c-injective if M is M-c-injective. For a projective module M, it has been proved that the factor module of an M -c-injective module is M -c-injective if and only if every closed submodule of M is projective. A characterization of self-c-injective modules in terms endomorphism ring of an R-module satisfying the CM-property is given.

Gorenstein σ[T]-injectivity on T-coherent rings

2015 ◽  
Vol 08 (04) ◽  
pp. 1550083 ◽  
Author(s):  
F. Shaveisi ◽  
M. Amini ◽  
M. H. Bijanzadeh
Keyword(s):  
Injective Module ◽  
Tilting Module ◽  
Basic Properties ◽  
Injective Modules ◽  
Coherent Rings

Let [Formula: see text] be a tilting module. In this paper, Gorenstein [Formula: see text]-injective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein [Formula: see text]-injective are given. For instance, we show that every [Formula: see text]-module is Gorenstein [Formula: see text]-injective if and only if every flat [Formula: see text]-module is Gorenstein [Formula: see text]-injective if and only if [Formula: see text] is a [Formula: see text]-injective module on itself.

Characterization of rings using finite-direct-injective modules

2019 ◽  
Vol 13 (07) ◽  
pp. 2050133
Author(s):  
Sanjeev Kumar Maurya ◽  
A. J. Gupta
Keyword(s):  
Injective Module ◽  
Artinian Rings ◽  
Injective Modules

In this paper, we characterize strongly right [Formula: see text]-rings in terms of finite-direct-injective modules which is a generalization of direct-injective modules (or [Formula: see text]-modules). Using this result, we give an example of a finite-direct-injective module which is not a direct-injective module. We prove that if every finite-direct-injective right [Formula: see text]-module is a direct-injective module, then the ring [Formula: see text] must be right Noetherian. Also, we characterize semisimple artinian rings, regular right FGC-rings in terms of finite-direct-injective modules.

scholarly journals KARAKTERISASI MODUL CYCLICALLY PURE (CP)-INJEKTIF

2020 ◽  
Vol 3 (1) ◽  
pp. 1-14
Author(s):  
Nia Yulianti ◽  
Hanni Garminia Y
Keyword(s):  
Commutative Ring ◽  
Injective Module ◽  
Injective Modules ◽  
Pure Extension

This research deals with the structure of cyclically pure injective modules over a commutative ring R. If I be an ideal of R, proved that any CP-injective R/Imodul is also CP-injective as an R-module. The main result of research is the existance of CP-injective R-module if there is an R-module. More over, we deal characterization of CP-injective module which is related to proper essential ctclically pure extension. It is shown that R-modul D is cyclically pure injective if and only if D has no proper essential cyclically pure extension.

Psq-injective modules and rings

2021 ◽  
pp. 2250101
Author(s):  
Avanish Kumar Chaturvedi ◽  
Sandeep Kumar
Keyword(s):  
Injective Module ◽  
Injective Modules

For any two right [Formula: see text]-modules [Formula: see text] and [Formula: see text], [Formula: see text] is said to be a ps-[Formula: see text]-injective module if, any monomorphism [Formula: see text] can be extended to [Formula: see text]. Also, [Formula: see text] is called psq-injective if [Formula: see text] is a ps-[Formula: see text]-injective module. We discuss some properties and characterizations in terms of psq-injective modules.

Strict Mittag–Leffler modules over Gorenstein injective modules

2019 ◽  
Vol 19 (03) ◽  
pp. 2050050 ◽  
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan
Keyword(s):  
Noetherian Ring ◽  
Direct Limit ◽  
Injective Module ◽  
Noetherian Rings ◽  
Projective Modules ◽  
Injective Modules ◽  
Pure Submodules ◽  
Covering Class ◽  
Gorenstein Injective ◽  
Finitely Presented

In this paper, we study the conditions under which a module is a strict Mittag–Leffler module over the class [Formula: see text] of Gorenstein injective modules. To this aim, we introduce the notion of [Formula: see text]-projective modules and prove that over noetherian rings, if a module can be expressed as the direct limit of finitely presented [Formula: see text]-projective modules, then it is a strict Mittag–Leffler module over [Formula: see text]. As applications, we prove that if [Formula: see text] is a two-sided noetherian ring, then [Formula: see text] is a covering class closed under pure submodules if and only if every injective module is strict Mittag–Leffler over [Formula: see text].

scholarly journals A Novel Approach towards Bipolar Soft Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Algebraic Structures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Novel Approach ◽  
Operational Laws

The notion of bipolar soft sets has already been defined, but in this article, the notion of bipolar soft sets has been redefined, called T-bipolar soft sets. It is shown that the new approach is more close to the concept of bipolarity as compared to the previous ones, and further it is discussed that so far in the study of soft sets and their generalizations, the concept introduced in this manuscript has never been discussed earlier. We have also discussed the operational laws of T-bipolar soft sets and their basic properties. In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.

scholarly journals Skew cyclic codes over 𝔽4R

2020 ◽  
pp. 2250065
Author(s):  
Nasreddine Benbelkacem ◽  
Martianus Frederic Ezerman ◽  
Taher Abualrub ◽  
Nuh Aydin ◽  
Aicha Batoul
Keyword(s):  
Error Control ◽  
Cyclic Codes ◽  
Gray Map ◽  
Inner Product ◽  
Algebraic Structures ◽  
Error Control Codes ◽  
Dna Codes ◽  
Natural Connection ◽  
Skew Cyclic Codes

This paper considers a new alphabet set, which is a ring that we call [Formula: see text], to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize [Formula: see text]-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over [Formula: see text] are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of [Formula: see text]-skew cyclic codes which are reversible complement.

scholarly journals Normal Toeplitz Operators on the Bergman Space

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1463
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Basic Properties

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).

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