The multiplicative behavior of ℋ

Abstract

ABSTRACT. Various results are given describing the product of two H-classes in an arbitrary semigroup in terms of groups and homomorphisms.1. It is known that in an arbitrary semigroup S the relation H of Green need not be a congruence: the product HK of two tf-classes H and K is usually spread out between several H-classes. Our main results give a fairly precise description of the set HK and the multiplication H x K -*■ HK. This is achieved by the first four of our five main theorems. Let {Rj)¡e¡, 0\)\ga he the families of all R-and L-classes which intersect HK. The first main theorem gives a partition of H into sets {Bj)iBI (and a partition of K into sets (YX