In this paper, we study hypergroups determined by lattices introduced by Varlet and Comer, especially we enumerate Varlet and Comer hypergroups of orders less than 50 and 13, respectively. 1 Basic definitions and results An algebraic hyperstructure is a natural generalization of a classical algebraic structure. More precisely, an algebraic hyperstructure is a non-empty set H endowed with one or...

The aim of this research work is to define a new class hyperstructure as generalization semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, fundamental relation on (Δ,G)-sets prove some results in respect. Then, introduce the notions quotient by using congruence relations. Finally, concept complete parts Noetherian(Artinian)

The homotopy hypothesis was originally stated by Grothendieck [13] : topological spaces should be “equivalent” to (weak) ∞-groupoids, which give algebraic representatives of homotopy types. Much later, several authors developed geometrizations of computational models, e.g. for rewriting, distributed systems, (homotopy) type theory etc. But an essential feature in the work set up in concurrency ...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

We consider a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined as follows: a P ∨ b = a ∨ b ∨ P , a Q ∧ b = a ∧ b ∧Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. We explore some properties of (L, P ∨, Q ∧) with special attention to various types of P ∨ and Q ∧ distributivity. AMS Subjec...

We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxe...

The study of BCK-algebras was initiated by Iséki [7] as a generalization of the concept of set-theoretic difference and propositional calculus. Iséki posed an interesting problem; whether the class of BCK-algebras is a variety. In connection with this problem Komori introduced in [9] a notion of BCC-algebra which is a generalization of a BCK-algebra and proved that the class of all BCC-algebras...

Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n–ary hyperstructures and binary relations we present a construction of n–ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a s...