REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In this talk we will describe a particular class of countably generated projective modules that was introduced by Prihoda in 2010. These are the so called I-big projective modules, where I refers to an idempotent ideal. For a ring R, the I-big projective modules can be understood as the lifting of the idempotents in the "stable category" to objects in Mod- R.

In the case of finitely generated algebras over a commutative Noetherian ring, relatively big projective modules allow a complete description of the objects in Add (M), for a finitely generated module M. This results in multiple applications to the study of direct summands of modules over commutative Noetherian local rings, over group algebras or, more generally, to the study of large lattices over orders.