The Cantor-Schröder-Bernstein Theorem in some categories of modules

Abstract

The Cantor-Schröder-Bernstein theorem has been studied in several categories throughout mathematics. In this article, we prove that this theorem holds in some relevant categories of modules, such as noetherian, and artinian, and prove that some strong versions of it also hold the category of finitely generated modules over a principal ideal domain.

Keywords

• Cantor-Schröder-Bernstein theorem
• Dedekind finite
• orthogonal modules
• chain conditions