Finitistic dimension through infinite projective dimension

TL;DR

This paper proves that artin algebras with limited layers of infinite projective dimension have finite finitistic dimension, extending previous results for algebras with a radical cube of zero.

Contribution

It generalizes the known finiteness of finitistic dimension from radical cube zero algebras to those with up to three layers of infinite projective dimension.

Findings

Artin algebras with at most three radical layers of infinite projective dimension have finite finitistic dimension.

Extension of the finiteness result from radical cube zero to more general radical layer conditions.

Provides new insights into the structure of algebras with finite finitistic dimension.

Abstract

We show that an artin algebra having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube.