Abstract
In this chapter, for a finite lattice K, we introduce an extension CubeK with the following properties: (i) The lattice K is a congruence-reflecting sublattice of CubeK. (ii) Con(CubeK) is boolean. (iii) The minimal extension of the meet-irreducible congruences are the dual atoms of Con(CubeK); their ordering is “flattened.”
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_________ , Congruence-preserving extensions of finite lattices into sectionally complemented lattices, Proc. Amer. Math. Soc. 127 (1999), 1903–1915.
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Grätzer, G. (2016). Cubic Extensions. In: The Congruences of a Finite Lattice. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-38798-7_7
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DOI: https://doi.org/10.1007/978-3-319-38798-7_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-38796-3
Online ISBN: 978-3-319-38798-7
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