### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 131-143 |

Number of pages | 13 |

Journal | Pacific Journal of Mathematics |

Volume | 77 |

Issue number | 1 |

State | Published - 1978 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Semigroups whose lattice of congruences is boolean'. Together they form a unique fingerprint.

## Cite this

Hamilton, H., & Nordahl, T. E. (1978). Semigroups whose lattice of congruences is boolean.

*Pacific Journal of Mathematics*,*77*(1), 131-143.