“An overview on non-unique factorizations”
Wednesday 2 October 2019, h. 16:00 - Room 2BC60 - Federico Campanini (Padova, Dip. Mat.)
In this seminar we present some basic facts about non-unique factorizations we hope will be interesting also for the non-algebraic audience. We start with the Fundamental Theorem of Arithmetic and we recall some elementary notions and examples on unique and non-unique factorization monoids. Then we move to the classical Krull-Schmidt Theorem for modules, which states that any module of finite length decomposes as a direct sum of indecomposable modules in an essentially unique way. We briefly discuss about some classes of modules in which direct-sum decompositions are not unique. Finally, we present some properties on factorizations in the monoid of polynomials with non-zero integral coefficients.