Operators coming from ring schemes

2020/08/19 by Jakub Gogolok, Gogolok, Jakub, Piotr A. Kowalski +1 · 1 citation
Mathematics · #03C45 #14L15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Primary 03C60 #Rings and Algebras (math.RA) #Secondary 12H05

paper · pdf · doi:10.48550/arxiv.2008.08443

openalex publication_date 2020/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a coordinate k-algebra scheme and the corresponding notion of a B-operator. This class of operators includes endomorphisms and derivations of the Frobenius map, and it also generalizes the operators related to D-rings from [15]. We classify the (coordinate) k-algebra schemes for a perfect field k and we also discuss the model-theoretic properties of fields with B-operators.

Cited by

• Forking independence in differentially closed fields of positive characteristic

Related

• Model theory of fields with free operators in positive characteristic
• The uniform companion for fields with free operators in characteristic zero
• Model theory of derivations of the Frobenius map revisited
• Classification of Boolean Algebras through von Neumann regular C^∞-Rings
• Introduction into Geometry over Division Ring