Subalgebras and finitistic dimensions of Artin algebras

TL;DR

This paper explores the properties of subalgebras within Artin algebras and identifies specific classes where the finitistic dimension is finite, advancing understanding of algebraic structure and homological dimensions.

Contribution

It introduces new conditions on subalgebras of Artin algebras that guarantee finite finitistic dimensions, expanding the classes of algebras with known homological properties.

Findings

Identified classes of subalgebras with finite finitistic dimensions

Established conditions ensuring finiteness of finitistic dimensions

Contributed to the classification of Artin algebras based on homological dimensions

Abstract

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.