24 citations · 68 across the 20 of their papers we have counts for
15 papers · 1 filter
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…
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…
Zero testing and equation solving for sparse polynomials on rectangular domains
Erhard Aichinger, Simon Grünbacher, Paul Hametner
We consider sparse polynomials in variables over a finite field, and ask whether they vanish on a set , where is a set of nonzero elements of the field. We see that if…
Finite representation of commutator sequences
Erhard Aichinger, Nebojša Mudrinski
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operati…
On the number of universal algebraic geometries
Erhard Aichinger, Bernardo Rossi
The algebraic geometry of a universal algebra is defined as the collection of solution sets of term equations. Two algebras and are calle…
Congruence preserving expansions of nilpotent algebras
Erhard Aichinger, Gábor Horváth
We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserv…