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Lattices of congruences on free finitely generated commutative semigroups and direct products of cyclic monoids
Published online by Cambridge University Press: 14 November 2011
Synopsis
Let S11× V1 be a direct product of a cyclic monoid S11with S1 not a group, and a semigroup V1 with an adjoined identity. We prove thatboth the lattice of congruences on (S11 × V1)/{(1,1)} and the lattice of congruences on (S11 × V1) are neither lower semimodular nor uppersemimodular. We then prove that the lattice of congruences on a free finitely generated commutative semigroup with more than one generator is neither lower semimodular nor upper semimodular.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 175 - 179
- Copyright
- Copyright © Royal Society of Edinburgh 1985
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