Characterizing noetherian rings via superstability

Abstract: We will show how superstability of certain classes of modules can be used to characterize noetherian rings. None of the classes of modules that we will consider are axiomatizable by a complete first-order theory and some of them are not even first-order axiomatizable, but they are all Abstract Elementary Classes (AECs). This new way of looking at classes of modules as AECs will be emphasized as I think it can have interesting applications. If time permits we will see how the ideas presented can be used to characterize other classical rings such as pure-semisimple rings and perfect rings.

commutative algebralogicrings and algebras

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic