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Regular congruence-preserving extensions of lattices

By G. Grätzer and E. T. Schmidt


In this paper, we prove that every lattice L has a congruencepreserving extension into a regular lattice ˜ L, moreover, every compact congruence of ˜ L is principal. We construct ˜ L by iterating a construction of the first author and F. Wehrung and taking direct limits. We also discuss the case of a finite lattice L, in which case ˜ L can be chosen to be finite, and of a lattice L with zero, in which case ˜ L can be chosen to have zero and the extension can be chosen to preserve zero

Year: 1999
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