A study of operands in terms of maximal generalized orbits

A left operand X of a monoid S is called saturated if every generalized orbit (g.o.) in X is contained in a union of others. Every operand has a natural decomposition as a union of an operand admitting an irredundant cover by maximal g.o. ′s and of a saturated operand. There is a descending chain of suboperands of an operand, defined in terms of maximal g.o. ′s, which leads to the definition of the saturation length of an operand. S has no saturated operands if and only if S satisfies the a.c.c. on orbits. Full proofs will be given in 2]. Communicated by A. H. Clifford