Document Type : Review Article

Author

• Elad Paran

The Open University of Israel

Abstract

In recent years there has been a flurry of activity surrounding non-commutative Nullstellens\"atze over the real quaternion algebra and over general division rings. From these results emerge rich arithmetic and geometry, which in many ways follow the classical themes and ideas of complex algebraic geometry, yet also exhibit new and interesting phenomena. In this survey we review developments in this active research area and discuss emerging open questions.

Keywords

• Division rings
• ring theory
• algebraic geometry
• Nullstellensatz