Polynomial interpolation of partial functions in finite algebras with a Mal'cev term
Rings and Algebras
2026-04-01 v1
Abstract
We provide polynomial completeness results for finite algebras in congruence permutable varieties. In 2001, Idziak and S{\l}omczy{\'n}ska introduced the completeness concept of being \emph{polynomially rich}: a finite algebra is polynomially rich if every function preserving congruences and the Tame Congruence Theory labelling of prime quotients in the congruence lattice is a polynomial function of the algebra. We call a finite algebra \emph{strictly polynomially rich} if every partial congruence and type preserving function is a polynomial function, and we describe strictly polynomially rich algebras in congruence permutable varieties.
Keywords
Cite
@article{arxiv.2603.29589,
title = {Polynomial interpolation of partial functions in finite algebras with a Mal'cev term},
author = {Erhard Aichinger and Mario Kapl and Bernardo Rossi},
journal= {arXiv preprint arXiv:2603.29589},
year = {2026}
}