Semigroups whose lattice of congruences is Boolean

H. B. Hamilton and T. E. Nordahl

Vol. 77 (1978), No. 1, 131–143

DOI: 10.2140/pjm.1978.77.131

Abstract

The commutative semigroups whose lattice of congruences forms a Boolean lattice are determined. They are (i) the null semigroups of order two or less, (ii) the discrete trees, (iii) the groups which are a direct sum of prime order cyclic groups in which no two factors have the same order, (iv) the semigroups which are a one element inflation of a discrete tree, (v) the semigroups which are a free product of a discrete tree with zero and a semigroup of type (iii) amalgamated over the trivial semigroup, and (vi) the semigroups which are a one element inflation of a semigroup of type (v).

Mathematical Subject Classification 2000

Primary: 20M14

Secondary: 06A12, 20M15

Milestones

Received: 26 April 1977

Revised: 16 November 1977

Published: 1 July 1978