Vol. 77, No. 1, 1978

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Semigroups whose lattice of congruences is Boolean

H. B. Hamilton and T. E. Nordahl

Vol. 77 (1978), No. 1, 131–143

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
Received: 26 April 1977
Revised: 16 November 1977
Published: 1 July 1978
H. B. Hamilton
T. E. Nordahl