Quotient bifinite extensions and the finitistic dimension conjecture

John William MacQuarrie; Fernando dos Reis Naves

Quotient bifinite extensions and the finitistic dimension conjecture

Representation Theory 2023-06-06 v1 Rings and Algebras

Authors: John William MacQuarrie , Fernando dos Reis Naves

Abstract

We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$ -bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$ . We exhibit examples demonstrating that the algebra $B$ appearing in such an extension can be more complicated than $A$ .

Keywords

finite-dimensional algebras extension theorems gorenstein-projective modules

Cite

@article{arxiv.2306.02539,
  title  = {Quotient bifinite extensions and the finitistic dimension conjecture},
  author = {John William MacQuarrie and Fernando dos Reis Naves},
  journal= {arXiv preprint arXiv:2306.02539},
  year   = {2023}
}

Comments

6 pages. To appear in Proceedings of the AMS

Quotient bifinite extensions and the finitistic dimension conjecture

Abstract

Keywords

Cite

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