A note on cancellation of reflexive modules

TL;DR

This paper investigates the conditions under which reflexive modules over affine rings can be canceled, providing new proofs under certain restrictions and counterexamples that show limitations without those assumptions.

Contribution

It establishes new cancellation results for reflexive modules over affine rings and presents counterexamples illustrating the boundaries of these results.

Findings

Cancellation holds under specific restrictions.

Counterexamples show failure without assumptions.

Provides new insights into reflexive module behavior.

Abstract

We prove that cancellation of reflexive modules over affine rings holds under some restrictions. We construct examples to show that this is false even over polynomial rings without the extra assumptions.