What are discrete valuation rings? What are Dedekind domains?

2021/02/20 by Aitken, Wayne
#Commutative Algebra (math.AC) #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2102.11725

Abstract

This is an extended introduction to discrete valuation rings and Dedekind domains. Some natural generalizations of Dedekind domains are also (briefly) discussed including "almost Dedekind domains", Prüfer domains, Krull domains, and singular integral domains of dimension 1.

Related

• Containment-Division Rings and New Characterizations of Dedekind Domains
• Simplicity of noncommutative Dedekind domains
• A valuation theorem for Noetherian rings
• Almost discrete valuation domains
• Arithmetical pseudo-valuations associated to Dubrovin valuation rings and prime divisors of bounded Krull domains