The Central Nullstellensatz over Centrally Algebraically Closed Division Rings

TL;DR

This paper introduces centrally algebraically closed division rings and proves their equivalence to division rings satisfying the central Nullstellensatz, also showing every division ring can embed into such a ring.

Contribution

It defines the concept of centrally algebraically closed division rings and establishes their fundamental properties and relation to the central Nullstellensatz.

Findings

Division rings satisfy the central Nullstellensatz iff they are centrally algebraically closed.

Every division ring can be embedded into a centrally algebraically closed division ring.

Abstract

We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebraically closed. We also show that every division ring can be embedded in a centrally algebraically closed division ring.