INVESTIGADORES
CAMPERCHOLI Miguel Alejandro Carlos
artículos
Título:
A short proof of the Baker-Pixley theorem for classes
Autor/es:
CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO
Revista:
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Editorial:
WORLD SCIENTIFIC PUBL CO PTE LTD
Referencias:
Año: 2023
ISSN:
0218-1967
Resumen:
An important theorem by Baker and Pixley states that if $mathbf{A}$ is a finite algebra with a $(d+1)$-ary near-unanimity term and $f:A^{n}ightarrow A$ is any function, then $f$ is a term-function of $mathbf{A}$ if $f$ preserves all subuniverses of $mathbf{A}^{d}$. This result was generalized recently for (classes of) not necessarily finite algebras using sheaf-theoretic tools. In this note 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 termto be congruence permutable.
