Nullstellensatz over quasifields

TL;DR

This paper explores differential rings of nonzero characteristic, introducing differentially closed quasifields and developing a geometric framework for differential equations in this setting, facilitating reduction modulo p.

Contribution

It introduces the concept of differentially closed quasifields and develops a geometric theory of differential equations in nonzero characteristic.

Findings

Development of the notion of differentially closed quasifields

Establishment of a geometric theory for differential equations in nonzero characteristic

Framework for reduction modulo p for differential equations

Abstract

We investigate the least studied class of differential rings -- the class of differential rings of nonzero characteristic. We present the notion of differentially closed quasifield and develop geometrical theory of differential equations in nonzero characteristic. The notions of quasivarieties and their morphisms are scrutinized. Presented machinery is a basis for reduction modulo p for differential equations.