Rigid integral representations of quivers over arbitrary commutative rings

TL;DR

This paper extends the classification of rigid quiver representations from principal ideal rings to arbitrary commutative rings, broadening the understanding of module representations over diverse ring structures.

Contribution

It introduces a classification of rigid quiver representations by finitely generated projective modules over any commutative ring, generalizing previous results.

Findings

Extended classification to arbitrary commutative rings

Included finitely generated projective modules

Broadened applicability of rigid representation theory

Abstract

In earlier work, the author classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. Here we extend the results to representations of a quiver by finitely generated projective modules over an arbitrary commutative ring.