Orador Convidado:

Pedro Macias Marques, Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora

Resumo:

In linear algebra, a Jordan basis is a generalisation of a basis ef eigenvectors of an endomorphism, and, unlike these, it always exsits, if we are working over an algebraically closed field.
If we consider the multiplication by a nilpotent element in an Artinian ring, we obtain an endomorphism whose only eigenvalue is zero. We can therefore define the Jordan type of this endomorphism from the sizes of the Jordan blocks in a Jordan matrix.
In this introductory talk, I will try to explain how we can use this invariant of an Artinian algebra, and look at a few open questions.
Resumo (pdf):

Em anexo.