Semigroups whose lattice of congruences is boolean

Howard Hamilton, Thomas E Nordahl

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)131-143
Number of pages13
JournalPacific Journal of Mathematics
Volume77
Issue number1
StatePublished - 1978
Externally publishedYes

Fingerprint

Congruence
Semigroup
Inflation
Boolean Lattice
Free Product
Cyclic group
Direct Sum
Null
Trivial
Zero

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Pacific Journal of Mathematics, Vol. 77, No. 1, 1978, p. 131-143.

Research output: Contribution to journalArticle

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