Some new classes of (m,n)-hyperrings

Jančić-Rašović, Sanja; Dasic, Vucic

doi:10.2298/fil1203585j

Cited by 5 publications

(4 citation statements)

References 7 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then the structure (N, + ≤ , • ≤ ) is a strongly distributive general hypernear-ring (in fact it is a hyperring). This follows from Theorem 4.3 [19]. Furthermore, for any a / ∈ N, it can be easily verified that (N, + ≤ ) is a proper subhypergroup of (N ∪ {a}, + ≤ ), where the hyperoperation + ≤ is defined by:…”

Section: Remark 1 Let (G +) Be a Group And T(g) Be The Transformations Near-ring On G Obviously T(g) ⊂mentioning

confidence: 76%

Weak Embeddable Hypernear-Rings

2019

View full text Add to dashboard Cite

In this paper we extend one of the main problems of near-rings to the framework of algebraic hypercompositional structures. This problem states that every near-ring is isomorphic with a near-ring of the transformations of a group. First we endow the set of all multitransformations of a hypergroup (not necessarily abelian) with a general hypernear-ring structure, called the multitransformation general hypernear-ring associated with a hypergroup. Then we show that any hypernear-ring can be weakly embedded into a multitransformation general hypernear-ring, generalizing the similar classical theorem on near-rings. Several properties of hypernear-rings related with this property are discussed and illustrated also by examples.

show abstract

Section: Remark 1 Let (G +) Be a Group And T(g) Be The Transformations Near-ring On G Obviously T(g) ⊂mentioning

confidence: 76%

Weak Embeddable Hypernear-Rings

2019

View full text Add to dashboard Cite

show abstract

“…The additive hyperrings (when the multiplication is weakly distributive over the hyperoperation) are also called hyperrings with inclusive distributivity, cf. Jančić-Rašović and Dašić [15][16][17]. On the other hand, the same term weak distributivity is used by Davvaz [8] (and later on by other researchers) to define the validity of the following relations on R: for any x, y, z ∈ R,…”

Section: Hypernear-rings: Terminology and Basic Resultsmentioning

confidence: 99%

Hypernear-rings with a defect of distributivity

Jančić-Rašović

Cristea

2018

Filomat

Self Cite

View full text Add to dashboard Cite

Since in a near-ring the distributivity holds just on one side (left or right), it seems naturally to study the behaviour and properties of the set of elements that "correct" the lack of distributivity, in other words that elements that assure the validity of the distributivity. The normal subgroup of the additive structure of a near-ring generated by these elements is called a defect of distributivity of the near-ring. The purpose of this note is to initiate the study of the hypernear-rings (generalizations of near-rings, having the additive part a quasicanonical hypergroup) with a defect of distributivity, making a comparison with similar properties known for near-rings.

show abstract

“…A special type of additive hyperring is the Krasner's hyperring and hyperfield [20,21,24,27,28]. The construction of different classes of hyperrings can be found in [29][30][31][32][33]. There are different kinds of curves that basically are used in cryptography [34,35].…”

Section: Introductionmentioning

confidence: 99%

Derived Hyperstructures from Hyperconics

et al. 2020

View full text Add to dashboard Cite

In this paper, we introduce generalized quadratic forms and hyperconics over quotient hyperfields as a generalization of the notion of conics on fields. Conic curves utilized in cryptosystems; in fact the public key cryptosystem is based on the digital signature schemes (DLP) in conic curve groups. We associate some hyperoperations to hyperconics and investigate their properties. At the end, a collection of canonical hypergroups connected to hyperconics is proposed.

show abstract

Some new classes of (m,n)-hyperrings

Cited by 5 publications

References 7 publications

Weak Embeddable Hypernear-Rings

Weak Embeddable Hypernear-Rings

Hypernear-rings with a defect of distributivity

Derived Hyperstructures from Hyperconics

Contact Info

Product

Resources

About