Regular Congruence-preserving Extensions of Lattices
نویسندگان
چکیده
In this paper, we prove that every lattice L has a congruencepreserving extension into a regular lattice L̃, moreover, every compact congruence of L̃ is principal. We construct L̃ 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 L̃ can be chosen to be finite, and of a lattice L with zero, in which case L̃ can be chosen to have zero and the extension can be chosen to preserve zero.
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تاریخ انتشار 1999