Uniformly Primal Submodule over Noncommutative Ring

Abulebda, Lamis J. M.

doi:10.1155/2020/1593253

Cited by 2 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2020, Razzaque et al [14], worked on soft LA-modules by defining projective soft LA-modules, free soft LA-modules, split sequence in soft LA-modules, and establish various results on projective and injective soft LA-modules. Abulebda in [15] discussed the uniformly primal submodule over noncommutative ring and generalized the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules. In [16], Groenewald worked on weakly prime and weakly 2-absorbing modules over noncommutative rings.…”

Section: Introductionmentioning

confidence: 99%

Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

Razzaque

Rehman

2022

Journal of Mathematics

View full text Add to dashboard Cite

The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the attention of many researchers over the last decade. In this study, the ideas of projective and injective LA-modules, LA-vector space, as well as examples and findings, are discussed. We construct a nontrivial example in which it is proved that if the LA-module is not free, then it cannot be a projective LA-module. We also construct free LA-modules, create a split sequence in LA-modules, and show several outcomes that are connected to them. We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.

show abstract

Section: Introductionmentioning

confidence: 99%

Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

Razzaque

Rehman

2022

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

On Radical of Intuitionistic Fuzzy Primary Submodule

Taherpour

Ghalandarzadeh

Rad

et al. 2022

Journal of Mathematics

View full text Add to dashboard Cite

In this paper, we further study the theory of Intuitionistic fuzzy submodules and we will define intuitionistic fuzzy primary submodule with the help of the definition of a radical submodule, and we also study the properties of these submodules. Furthermore, homomorphic image and preimage of intuitionistic fuzzy primary submodule are investigated. This manuscript is online on arXiv by the link https://arxiv.org/abs/2207.09772.

show abstract

Uniformly Primal Submodule over Noncommutative Ring

Abstract: Let R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N , if there exists an element … Show more

Cited by 2 publications

References 14 publications

Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

On Radical of Intuitionistic Fuzzy Primary Submodule

Contact Info

Product

Resources

About