Quotient bifinite extensions and the finitistic dimension conjecture

Abstract

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