Level and Gorenstein Projective Dimension

TL;DR

This paper explores the connection between the level of bounded complexes over commutative rings relative to Gorenstein projective modules and various algebraic invariants, extending previous work on projective modules.

Contribution

It introduces new relationships between Gorenstein projective levels and invariants like projective and Gorenstein projective dimensions, generalizing prior results.

Findings

Established bounds relating Gorenstein projective level to projective dimension.

Extended classical results to the Gorenstein context.

Provided new insights into the structure of complexes over commutative rings.

Abstract

We investigate the relationship between the level of a bounded complex over a commutative ring with respect to the class of Gorenstein projective modules and other invariants of the complex or ring, such as projective dimension, Gorenstein projective dimension, and Krull dimension. The results build upon work done by J. Christensen [6], H. Altmann et al. [1], and Avramov et al. [3] for levels with respect to the class of finitely generated projective modules.