Vol. 77, No. 1, 1978

Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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