This article is cited in 6 papers

Lattices Embeddable in Subsemigroup Lattices. II. Cancellative Semigroups

M. V. Semenova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Repnitskii proved that any lattice embeds in a subsemigroup lattice of some commutative, cancellative, idempotent free semigroup with unique roots. In that proof, use is made of a result by Bredikhin and Schein stating that any lattice embeds in a suborder lattice of suitable partial order. Here, we present a direct proof of Repnitskii's result which is independent of Bredikhin–Schein's, thus giving the answer to the question posed by Shevrin and Ovsyannikov.

Keywords: commutative semigroup, subsemilattice lattice.

UDC: 512.56

Received: 05.10.2005
Revised: 02.02.2006

 English version: Algebra and Logic, 2006, 45:4, 248–253

Bibliographic databases:

• 
• 
•