We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when non-empty subset is base. Moreover, we give characterization base to be subsemigroup show that have same cardinality. Finally, complement union all maximal proper left ideal.

A semigroup S is called locally finite (respectively, periodic) if each finitely generated (respectively, each monogenic) subsemigroup in S is finite. A semigroup variety is locally finite (respectively, periodic) if so are all its members. Clearly, every locally finite variety is periodic but the converse is not true. The issues related to determining extra properties that distinguish locally ...

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...

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...

Abstract We are interested in properties, especially injectivity (in the sense of category theory), ternary rings operators generated by certain subsets an inverse semigroup via regular representation. determine all extended bicyclic which closed under triple product $$xy^*z$$ x y <...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...