Characterizing representability by principal congruences for finite\n distributive lattices with a join-irreducible unit element

2021/04/28 by George Grätzer, Grätzer, George
Computer Science · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2104.14048

Abstract

For a finite distributive lattice D, let us call Q \⊆ D\n\principal congruence representable, if there is a finite lattice L\nsuch that the congruence lattice of L is isomorphic to D and the principal\ncongruences of L correspond to Q under this isomorphism.\n We find a necessary condition for representability by principal congruences\nand prove that for finite distributive lattices with a join-irreducible unit\nelement this condition is also sufficient.\n

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