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

TL;DR

This paper proves that the entire theory of modules over the ring of algebraic integers is decidable, providing a significant result in the field of algebra and logic.

Contribution

It establishes the decidability of the theory of modules over the ring of algebraic integers, a previously unresolved problem.

Findings

The theory of modules over the ring of algebraic integers is decidable.

Decidability results for algebraic structures over rings of algebraic integers.

Advances understanding of logical properties of modules over complex rings.

Abstract

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