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- Title
A short proof of the Baker–Pixley theorem for classes.
- Authors
Campercholi, Miguel; Vaggione, Diego
- Abstract
An important theorem by Baker and Pixley states that if A is a finite algebra with a (d + 1) -ary near-unanimity term and f : A n → A is any function, then f is a term-function of A if f preserves all subuniverses of A d . This result was generalized recently for (classes of) not necessarily finite algebras using sheaf-theoretic tools. In this work, we give a short model-theoretic proof of this generalization. Also, we apply the theorem to obtain a characterization of dual discriminator varieties, and to give necessary and sufficient conditions for a variety with a near-unanimity term to be congruence permutable.
- Subjects
ALGEBRA; GENERALIZATION; GEOMETRIC congruences
- Publication
International Journal of Algebra & Computation, 2023, Vol 33, Issue 8, p1651
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196723500625