Literature Survey on Non-Associative Rings and Developments

Shah, Syed Tariq; Razzaque, Asima; Rehman, Inayatur; Gondal, Muhammad Asif; Faraz, Muhammad Iftikhar; Shum, K. P.

doi:10.29020/nybg.ejpam.v12i2.3408

Cited by 4 publications

(7 citation statements)

References 171 publications

(193 reference statements)

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“…Reference [1] shows that Jordan ring can be constructed from any ring. For any ring R one can define the Jordan product as follow for each r 1 , r 2 ∈ R, r 1 • r 2 = r 1 r 2 + r 2 r 1 .…”

Section: Non-associative Ringsmentioning

confidence: 99%

“…Several researchers have investigated non-associative rings, for examples Shah [1] and Razzaque [2]. Reference [1] explains a survey of non-associative rings.…”

Section: Introductionmentioning

confidence: 99%

“…Several researchers have investigated non-associative rings, for examples Shah [1] and Razzaque [2]. Reference [1] explains a survey of non-associative rings. It is mentioned here that some examples of non-associative rings are octonions, Lie rings, alternative rings, Jordan rings, and loop rings.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we investigate the Jordan ring which is nonassociative, commutative, and preserves the Jordan identity. Jordan ring also can be constructed from any ring A [1]. If A is commutative, then a Jordan ring formed is associative, but the converse is not always true.…”

Section: Introductionmentioning

confidence: 99%

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On Non-Associative Rings

Waliyanti¹,

Wijayanti²,

Rosyid³

2021

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Section: Non-associative Ringsmentioning

confidence: 99%

“…Several researchers have investigated non-associative rings, for examples Shah [1] and Razzaque [2]. Reference [1] explains a survey of non-associative rings.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Non-Associative Rings

Waliyanti¹,

Wijayanti²,

Rosyid³

2021

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“…Moreover, Zhan and Tan [10] introduced the notion of left weakly Novikov algebra. In many fields (such as non-associative rings and non-associative algebras [11][12][13][14]), image processing [15], and networks [16]), non-associativity has essential research significance. Since cyclic associative law is widely used in algebraic systems, we have been focusing on the basic algebraic structure of cyclic associative groupoids (CA-groupoids) and other relevant algebraic structures (see [17,18]).…”

Section: Introductionmentioning

confidence: 99%

Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

Yuan

Zhang

2020

Mathematics

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Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is a regular CA-groupoid if and only if it is a CA-NET-groupoid; (2) if (S, *) is a regular CA-groupoid, then every element of S lies in a subgroup of S, and every ℋ -class in S is a group; and (3) an algebraic system is an inverse CA-groupoid if and only if it is a regular CA-groupoid and its idempotent elements are commutative. Moreover, the Green relations of CA-groupoids are investigated, and some examples are presented for studying the structure of regular CA-groupoids.

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

Razzaque

Rehman

2022

Journal of Mathematics

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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.

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Literature Survey on Non-Associative Rings and Developments

Cited by 4 publications

References 171 publications

On Non-Associative Rings

On Non-Associative Rings

Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

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

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