Aczélian n-ary semigroups

On absorption in semigroups and n-ary semigroups

The notion of absorption was developed a few years ago by Barto and Kozik and immediately found many applications, particularly in topics related to the constraint satisfaction problem. We investigate the behavior of absorption in semigroups and n-ary semigroups (that is, algebras with one n-ary associative operation). In the case of semigroups, we give a simple necessary and sufficient conditi...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

n–ary hyperstructures constructed from binary quasi–ordered semigroups

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...

On the n-ary algebras, semigroups and their universal

For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups. AMS Classification: 17A42, 16N34, 20N15

Generalization of Czogała-Drewniak Theorem for n-ary Semigroups

We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X ,Fn), where X is a set and an n-associative function Fn : Xn → X is defined on X . We show that if Fn is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I ⊂ R and has a neutral element, then Fn is combination of the minimum and maximum ...