Idempotent semigroups generated by threads i

Abstract

are idempotent with identity element 1, and have threads A and B with 1 ~ A n B and S = AB. Our main result is a characterization of such semigroups S with S/K commutative, and we show the equivalence of this property with the identity xyz = xy, xz or yz. In analogy with the case of semilattices, we say that S has breadth 2 if it satisfies this identity. Schein and others have called such semigroups exclusive (see, for example, [3]). We show further that S/K is commutative if and only if S is the continuous homomorphic image of