In this paper we study certain types of positive fuzzy quasi-orders on semigroups and their links with completely semiprime ideals, prime filters. We characterize various properties a quasi-order Q in terms the its left right eigen spaces IQ CQ, solution sets set equations corresponding to Q. also demonstrate applications obtained results semilattice decompositions semigroups. The shed new ligh...

In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

We find all finite unavoidable ordered sets, finite unavoidable semilattices and finite unavoidable lattices.

For a nonempty set X, let T(X) be the total transformation semigroup on X. In this paper, we consider subsemigroups of which are defined by T(X,Y) ={α∈T(X):Xα⊆Y}andS(X,Y)={α∈T(X):Yα⊆Y} where Y is non-empty subset We characterize left regular and right elements both S(X,Y). Moreover, necessary sufficient conditions for S(X,Y) to given. These results then applied determine numbers in finite

Abstract A semigroup S is said to be left equalizer simple if, for all elements a , b x y of $$xa=xb$$ x a = b implies $$ya=yb$$ y . It known that simplicity necessary condition embedded in semigroup. satisfying the ide...

We investigate definability in the set of isomorphism types of finite semilattices ordered by embeddability; we prove, among other things, that every finite semilattice is a definable element in this ordered set. Then we apply these results to investigate definability in the closely related lattice of universal classes of semilattices; we prove that the lattice has no non-identical automorphism...