The semilattice equivalence relations play an important role in investigating the structural properties of ordered semihypergroups. Such can be expressed terms hyperfilters. There are two concepts (ordered) hyperfilters semihypergroups which were introduced by Tang et al. [16] and Kehayopulu[9]. In this paper, we prove that those coincide characterize least on Furthermore, investigate relations...

An inverse semigroup is a semigroup S such that for each x e S there exists a unique inverse x~ & S such that both xx~x=x and x~xx~=x~\ This condition is equivalent to S both being (von Neumann) regular and having all idempotents commute. The classic example of such a semigroup is the symmetric inverse semigroup Ix of all partial bijections on a set X under the standard composition of partial f...

i.e., each principal filter is pseudo-complemented. Based on the way relatively complemented lattices are defined (every interval is complemented), this seemed like the natural way to define relatively pseudocomplemented (for a lattice with a greatest element, (1) is equivalent to each each interval being pseudo-complemented). However, the term relatively pseudo-complemented was already in use ...

We study the class of symmetric [Formula: see text]-ary bands. These are semigroups text] such that is invariant under action permutations and idempotent, i.e., satisfies for all text]. first provide a structure theorem these bands extends classical (strong) semilattice decomposition certain classes introduce concept strong we show exactly semilattices extensions Abelian groups whose exponents ...