On the decidability of the theory of modules over the ring of algebraic\n integers

2016/03/30 by Sonia L’Innocente, L'Innocente, Sonia, Carlo Toffalori +3
Computer Science · Mathematics · #03B25 #03C98 #13C11 #Advanced Algebra and Logic #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1603.09042

openalex publication_date 2016/03/30 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We prove that the theory of all modules over the ring of algebraic integers is decidable.

Related

• The Theory of the Entire Algebraic Functions
• Defining \mathbb Z using unit groups
• Indecomposable Algebraic Integers
• Computation of the classifying ring of formal modules
• First Order Decidability and Definability of Integers in Infinite Algebraic Extensions of Rational Numbers