Seminario Teoría de Grupos
A study of Sylvester rank functions via functor categories
Ponente: Simone Virili (Universidad Autónoma de Barcelona)Fecha: miércoles 29 de octubre de 2025 - 16:00Lugar: Aula Naranja, ICMAT
Resumen:
Given a ring R, a Sylvester rank function on the category of finitely presented right R-modules is an isomorphism-invariant function which is additive on coproducts, subadditive on right-exact sequences, monotone on quotients, and taking the value 1 on R.
In this talk I will start by observing that any Sylvester rank function can be uniquely extended to a so-called length function on the category of functors from finitely presented left R-modules to Abelian groups. This enlargement of the setting comes with many advantages and, to illustrate this, I will provide examples of results about rank functions whose initial proofs are technically demanding, yet can be derived almost effortlessly within the expanded framework.
