Erhard Aichinger, Bernardo Rossi,
"On the number of universal algebraic geometries"
, in Algebra Universalis, Vol. 84, Nummer pub. online on Nov 28, 2022, Seite(n) paper no. 1, 2023, ISSN: 0002-5240
On the number of universal algebraic geometries
Sprache des Titels:
The algebraic geometry of a universal algebra A is defined
as the collection of solution sets of systems of term equations. Two
algebras are called algebraically equivalent if they have the
same algebraic geometry. We prove that on a finite set A with |A| > 3
there are countably many algebraically inequivalent Mal?cev algebras
and that on a finite set A with |A| > 2 there are continuously many
algebraically inequivalent algebras.