First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

In studying a general semigroup S, a natural thing to do is to decompose 5 (if possible) into the class sum of a set {Sa; aCl} of mutually disjoint subsemigroups Sa such that (1) each Sa belongs to some more or less restrictive type 13 of semigroup, and (2) the product SaSfi of any two of them is wholly contained in a third: SaSpClSy, for some yCI depending upon a and /3. We shall then say that...

A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.

Given a Banach space X, denote by SPw(X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X. It is known that SPw(X) is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphi...

We begin by recalling the general theory of adjoints on finite semilattices. A finite join semilattice with 0 is a lattice, with the naturally induced meet operation. Thus a finite lattice S can be regarded as a semilattice in two ways, either S = 〈S,+, 0〉 or S = 〈S,∧, 1〉. Given a (+, 0)-homomorphism g : S → T , define the adjoint h : T → S by h(t) = ∑ {s ∈ S : gs ≤ t} so that gs ≤ t iff s ≤ ht...

We describe the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY whereX and Y are certain totally ordered topological spaces, and where βoZ denotes the Stone–Čech orderedor Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY for arbitrary totally ordered topol...