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...

J. Rhodes asked during the Chico conference in 1986 for the calculation of joins of semigroup pseudovarieties. This paper proves that the join J∨V of the pseudovariety J of J -trivial semigroups and of any 2-strongly decidable pseudovariety V of completely regular semigroups is decidable. This problem was proposed by the first author for V = G, the pseudovariety of finite groups.