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arXiv · 2603.29589

Polynomial interpolation of partial functions in finite algebras with a Mal'cev term

Erhard Aichinger·Mario Kapl·Bernardo Rossi
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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.

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Erhard Aichinger, Mario Kapl, Bernardo Rossi. 2026-03-31. Polynomial interpolation of partial functions in finite algebras with a Mal'cev term. https://arxiv.org/abs/2603.29589

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