The ℛ-height of semigroups and their bi-ideals

Abstract

The [Formula: see text]-height of a semigroup [Formula: see text] is the height of the poset of [Formula: see text]-classes of [Formula: see text] Given a semigroup [Formula: see text] with finite [Formula: see text]-height, we establish bounds on the [Formula: see text]-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite [Formula: see text]-height. We then investigate whether these bounds can be attained.