Changchang Xi (Capital Normal University, Beijing)

Finitistic dimensions and radical-power extensions

Abstract:

In this talk, we report some new results (jointly with Chengxi Wang) on controlling the finitistic dimensions of smaller algebras by the ones of bigger algebras for extensions of Artin algebras. More precisely, we consider the question: How to bound the finitistic dimension of a subalgebra by the one of a given algebra if some power of the radical of the subalgebra is a one-sided ideal in the given algebra? Our results generalize some of the known ones in the literature and provide new methods to test finiteness of finitistic dimensions of algebras.