Classifications of (α,β )-fuzzy left (right and lateral) ideals of ternary semigroups are discussed. Relations between (∈,∈ ∨q)-fuzzy left (right and lateral) ideals and (q,∈∨q)-fuzzy left (right and lateral) ideals are established. Given special sets, so called t-q-set and t-∈∨q-set, conditions for the t-q-set and t-∈∨q-set to be left (right and lateral) ideals are considered. Conditions for a...

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...

In this study, Bruck-Reilly extension of a ternary monoid is defined. Additionally, some results about construction are given which belongs to one the classes semigroups; regular, inverse, orthodox and strongly regular.

Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of v...