The geometry of a clone

Description

The \emph{algebraic geometry} of a clone $C$ on a set $A$, denoted by $\Alg C$, is defined as the collection of solution sets of systems of $C$-equations. Hence it is a subset of $\bigcup_{n\in \N}\potenza{A}$. Classical algebraic geometry can be viewed as the study of $\Alg\POL(\ab{K})$, where $\ab{K}$ is a field. In the talk a general introduction to the topic will be given. In particular we will discuss the properties of the algebraic geometry of the clones on the two element set; the number of distinct algebraic geometries over a finite set; and the relationship between closure properties of the algebraic geometry of a constantive Mal'cev clone and the term condition commutator.\\ The unpublished results presented in this talk are joint work with E. Aichinger and M. Behrisch and supported by the Austrian Science Fund (FWF): P33878.

Period	25 Jul 2022
Event title	unbekannt/unknown
Event type	Other
Location	ItalyShow on map