In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...

We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice L is well-founded if and only if K(L), the join-semilattice of compact elements of L, is well-founded and contains neither [ω], nor Ω(ω∗) as a join-subsemilattice. As an immediate corollary, we get that...

For a class V of algebras, denote by Conc V the class of all (∨, 0)semilattices isomorphic to the semilattice Conc A of all compact congruences of A, for some A in V. For classes V1 and V2 of algebras, we denote by crit(V1;V2) the smallest cardinality of a (∨, 0)-semilattice in Conc V1 which is not in Conc V2 if it exists, ∞ otherwise. We prove a general theorem, with categorical flavor, that i...

We study completely π-regular semigroups admitting a decomposition into a semilattice of σn-simple semigroups, and describe them in terms of properties of their idempotents. In the general case, semigroups admitting a decomposition into a semilattice of σn-simple semigroups were characterized by M. Ćirić and S. Bogdanović in [3] (see Theorem 1 below), in terms of paths of length n in the graph ...