Online algebra seminar - November 12th, 1pm PDF Print

We will continue online on Thursday, November 12th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Marcos Mazari-Armida (Carnegie Mellon University)

Model-theoretic stability and superstability in classes of modules

Dividing lines in complete first-order theories were introduced by Shelah in the early seventies. A dividing line is a property such that the classes satisfying such a property have some nice behaviour while those not satisfying it have a bad one. Two of the best understood dividing lines are those of stability and superstability.
In this talk, I will study the notion of stability and superstability in abstract elementary classes of modules with respect to pure embeddings, i.e., classes of the form (K,≤p) where K is a class of R-modules for a fixed ring R and ≤p is the pure submodule relation. In particular, using that the class of p-groups with pure embed- dings is a stable AEC, I will present a solution to Problem 5.1 in page 181 of Abelian Groups by Laszlo Fuchs. Moreover, I will show how the notion of superstability can be used to give new characterizations of noetherian rings, pure-semisimple rings, and perfect rings.

Last Updated on Tuesday, 10 November 2020 15:14