Finite generation of congruence preserving functions
نویسندگان
چکیده
منابع مشابه
Congruence Preserving Functions on Free Monoids
A function on an algebra is congruence preserving if, for any congruence, it maps congruent elements to congruent elements. We show that, on a free monoid generated by at least three letters, a function from the free monoid into itself is congruence preserving if and only if it is of the form x 7→ w0xw1 · · ·wn−1xwn for some finite sequence of words w0, . . . , wn. We generalize this result to ...
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We prove that every finite lattice has a congruence-preserving extension to a finite semimodular lattice.
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In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving ex...
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We call a lattice L isoform, if for any congruence relation Θ of L, all congruence classes of Θ are isomorphic sublattices. In an earlier paper, we proved that for every finite distributive lattice D, there exists a finite isoform lattice L such that the congruence lattice of L is isomorphic to D. In this paper, we prove a much stronger result: Every finite lattice has a congruence-preserving e...
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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 ...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2015
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-015-0833-5