Three-element bands in βN

摘要

Let N be the discrete additive semigroup of natural numbers and let βN be the Stone-Čech compactification of N.The addition on N extends to an operation + on βN making it a right topological semigroup, and to an operation ∗ making it a left topological semigroup. The semigroup (βN,∗) is the opposite of the semigroup (βN,+): p∗ q=q+p. We list all 3-element idempotent semigroups that have algebraic copies in (βN,+).As a consequence we obtain that (βN,+) and (βN,∗) are not algebraically isomorphic.