Abstract
Let 〈V; ∪, ∩〉 be a lattice, thenF(V), the set of all functions fromV toV, becomes a lattice by defining the operations ∪ and ∩ pointwise. If we also consider the composition of functions as an operation onF(V), we get the function algebra 〈F(V); ∪, ∩,·〉. In this paper we give a characterization of the lattices with nonsimple function algebras. Moreover, the congruence lattice of these function algebras turns out to be a three-element chain.
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Literatur
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Karigl, G. Die Verbände mit nichteinfacher Funktionenalgebra. Monatshefte für Mathematik 84, 289–302 (1977). https://doi.org/10.1007/BF01366498
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DOI: https://doi.org/10.1007/BF01366498