Foundations of Ordered (Semi)hyperrings

Davvaz, Bijan; Omidi, Saber

doi:10.22342/jims.22.2.233.131-150

Search citation statements

Order By: Relevance

Paper Sections

Select...

Discussion2

Preliminaries1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(3 citation statements)

References 15 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By routine calculations, H is a hyper BN -algebra. Define a relation θ on H by θ = {(0, 0), (0, 2), (1,1), (1,3), (2, 0), (2,2), (3,1), (3,3), (4,4)}. By inspection, θ is an equivalence relation on H. Now, observe that 1θ3 and 2θ0 but 1 ⊛ 2 = {2}̸ θ{3} = 3 ⊛ 0 because (2, 3) / ∈ θ.…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals

Cabardo,

Petalcorin Jr.

2024

Eur. J. Pure Appl. Math.

View full text Add to dashboard Cite

A hyper $BN$-algebra is a nonempty set $H$ together with a hyperoperation ``$\circledast$'' and a constant $0$ such that for all $x, y, z \in H$: $x \ll x$, $x \circledast 0 = \{x\}$, and $(x \circledast y) \circledast z = (0 \circledast z) \circledast (y \circledast x)$, where $x \ll y$ if and only if $0 \in x \circledast y$. We investigated the structures of ideals in the Hyper $BN$-algebra setting. We established equivalency of weak hyper $BN$-ideals and hyper sub$BN$-algebras. Also, we found a condition when a strong hyper $BN$-ideal become a hyper $BN$-ideal. Finally, we looked at two ways in constructing the quotient hyper $BN$-algebras and investigated the relationship between the two constructions.

show abstract