Polymorphism-homogeneity and universal algebraic geometry
We assign a relational structure to any finite algebra in a canonical way,using solution sets of equations, and we prove that this relational structureis polymorphism-homogeneous if and only if the algebra itself ispolymorphism-homogeneous. We show that polymorphism-homogeneity is alsoequivalent to...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2022
|
| Sorozat: | DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
23 No. 2 |
| Tárgyszavak: | |
| doi: | 10.46298/dmtcs.6904 |
| mtmt: | 33572459 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/28144 |
| Tartalmi kivonat: | We assign a relational structure to any finite algebra in a canonical way,using solution sets of equations, and we prove that this relational structureis polymorphism-homogeneous if and only if the algebra itself ispolymorphism-homogeneous. We show that polymorphism-homogeneity is alsoequivalent to the property that algebraic sets (i.e., solution sets of systemsof equations) are exactly those sets of tuples that are closed under thecentralizer clone of the algebra. Furthermore, we prove that the aforementionedproperties hold if and only if the algebra is injective in the category of itsfinite subpowers. We also consider two additional conditions: a strongervariant for polymorphism-homogeneity and for injectivity, and we describeexplicitly the finite semilattices, lattices, Abelian groups and monounaryalgebras satisfying any one of these three conditions. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 18 |
| ISSN: | 1462-7264 |