episciences.org_6904_1669548612
1669548612
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
03
21
2022
vol. 23 no. 2, special issue...
Special issues
Polymorphismhomogeneity and universal algebraic geometry
Endre
Tóth
Tamás
Waldhauser
We assign a relational structure to any finite algebra in a canonical way,
using solution sets of equations, and we prove that this relational structure
is polymorphismhomogeneous if and only if the algebra itself is
polymorphismhomogeneous. We show that polymorphismhomogeneity is also
equivalent to the property that algebraic sets (i.e., solution sets of systems
of equations) are exactly those sets of tuples that are closed under the
centralizer clone of the algebra. Furthermore, we prove that the aforementioned
properties hold if and only if the algebra is injective in the category of its
finite subpowers. We also consider two additional conditions: a stronger
variant for polymorphismhomogeneity and for injectivity, and we describe
explicitly the finite semilattices, lattices, Abelian groups and monounary
algebras satisfying any one of these three conditions.
03
21
2022
6904
https://arxiv.org/licenses/nonexclusivedistrib/1.0
arXiv:2007.04405
10.48550/arXiv.2007.04405
https://arxiv.org/abs/2007.04405v2
https://arxiv.org/abs/2007.04405v1
10.46298/dmtcs.6904
https://dmtcs.episciences.org/6904

https://dmtcs.episciences.org/9211/pdf