On the representation of lattices by subsemigroup lattices of bands (Q1902170)

The main results of the paper are Theorems 1 and 2. Theorem 1 gives a description of (finite) lattices which are embeddable in subsemigroup lattices of (finite) rectangular bands. Theorem 2 describes simple finite lattices which are embeddable in subsemigroup lattices of finite bands. As a corollary of Theorem 2 the author proves that the partition lattice of a set with \(\geq 3\) elements cannot be embeddable in the subsemigroup lattice of a finite band.