On endomorphism monoids in varieties of bands

Abstract

It will be proved that every non-trivial variety V of bands (idempotent semigroups) contains a proper generating class of non-isomorphic bands B such that B generates V and any band B' having the same endomorphism monoid as B is isomorphic to B or to the opposite band B^op. Consequently, every sharply greater band variety has a sharply greater class of endomorphism monoids.

Keywords

• endomorphism monoids
• varieties of bands