Román Álvarez (Universitat Autònoma de Barcelona)
Non-Finitely Generated Projective Modules over Integral Group Rings
Abstract: We introduce a relative version of the big projective modules introduced by Bass, which is an example of a non-finitely generated projective module. We develop the general theory of I-big projective modules introduced by Pavel Príhoda (2010). We inquire more deeply in a correspondence between countably generated projective modules over a ring R and finitely generated projective modules over a ring R modulo an ideal I and generalize it into an equivalence of categories as it is done by Herbera-Príhoda-Wiegand in a recent preprint (2020). Finally, we approach I-big projective modules over well-known rings in order to give an explicit example of the construction of non-finitely generated projective modules over the integral group ring ZA5, where A5 denotes the alternating group on 5 letters.