Extensions of algebras and preservation of the finitude of the finitistic dimension

An extension of (unital, associative) algebras is simply an algebra A with subalgebra B.  I will discuss two projects relating the homological properties of A and B under certain assumptions on the extension.  In a sequence of articles,Cibils, Lanzilotta, Marcos e Solotar prove that both the finitude of the global dimension and of the support of the Hochschild homology are preserved by what they call "bounded extensions".  In joint work with Kostiantyn Iusenko, we extend this result to a wider class of extensions that includes certain infinite dimensional extensions of interest to us (we allow, for instance, (completed) path algebras with loops and cycles).  We also add to the list the preservation of the finitude of the finistisic dimension.  These results have the form "A has a property iff B does".  The second project, joint work with Fernando dos Reis Naves, considers the question "If A has finite finitistic dimension, when can we say that B does too?": I'll show that the hypotheses on the extension can be weakened considerably.