Torsion-Free Modules with Nearly Unique Endomorphism Algebras

Abstract

Let R be a discrete valuation domain and n ≥ 1. If the completion of R contains at least n algebraically independent elements over R, then there exists a torsion-free module M such that End _R M is isomorphic to End _R N for exactly 2 ⁿ pairwise nonisomorphic modules N.

Key Words:

• Torsion-free
• Discrete valuation domain
• Endomorphism algebra

Acknowledgments