### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*77*(1), 131-143.

**Semigroups whose lattice of congruences is boolean.** / Hamilton, Howard; Nordahl, Thomas E.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 77, no. 1, pp. 131-143.

}

TY - JOUR

T1 - Semigroups whose lattice of congruences is boolean

AU - Hamilton, Howard

AU - Nordahl, Thomas E

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972541022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972541022&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972541022

VL - 77

SP - 131

EP - 143

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -