Dimension of finite free complexes over commutative Noetherian rings

TL;DR

This paper shows that the dimension of a bounded complex of finite free modules over a Noetherian ring can be directly computed from the matrices of its differentials, simplifying the understanding of such complexes.

Contribution

It introduces a method to compute the dimension of finite free complexes directly from differential matrices, extending Foxby's dimension concept.

Findings

Dimension can be computed from differential matrices

Simplifies analysis of finite free complexes

Extends Foxby's dimension concept

Abstract

Foxby defined the (Krull) dimension of a complex of modules over a commutative Noetherian ring in terms of the dimension of its homology modules. In this note it is proved that the dimension of a bounded complex of free modules of finite rank can be computed directly from the matrices representing the differentials of the complex.