The Central Nullstellensatz over Centrally Algebraically Closed Division Rings

2025/06/18 by Masood Aryapoor, Aryapoor, Masood
Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.2506.15187

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

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.

Citations

• Hilbert's Nullstellensatz over quaternions
• Shirshov's theorem and division rings that are left algebraic over a subfield
• Wedderburn polynomials over division rings, II
• Wedderburn Polynomials over Division Rings
• Wedderburn polynomials over division rings, I

Related

• A non-commutative Nullstellensatz
• Division Rings with Ranks
• Centrally Essential Rings and Semirings
• Linear groups over a locally linear division ring
• Centrality and Partition of Idempotents