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math.RA2026
Polynomial interpolation of partial functions in finite algebras with a Mal'cev term
Erhard Aichinger, Mario Kapl, Bernardo Rossi
We provide polynomial completeness results for finite algebras in congruence permutable varieties. In 2001, Idziak and Słomczy{ń}ska introduced the completeness concept of being \e…
math.RA2023
On polynomial completeness properties of finite Mal'cev algebras
Bernardo Rossi
Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not…
math.RA2023
On when the union of two algebraic sets is algebraic
Erhard Aichinger, Mike Behrisch, Bernardo Rossi
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to poly…