Seminario Dottorato: Regular biproduct decompositions of objects

Wednesday 14 December 2011 - Nicola Girardi

ARGOMENTI: Seminari Dottorato

Wednesday 14 December 2011 h. 15:00, room 2BC/30
Nicola GIRARDI (Padova, Dip. Mat.)
"Regular biproduct decompositions of objects"

Abstract. Every vector space over a field K is the direct sum of a number of copies of the one-dimensional K-vector space K. Allowing scalars to be elements of a ring R instead of a field, we obtain a more general object called right (or left, depending on which side we write the scalars) R-module. Contrary to the trivial case of K-vector spaces, modules over R may or may not decompose into indecomposable submodules, and when they do, it is interesting to know whether their decompositions are unique in some sense or at least satisfy some sort of constraint. Beginning with the basics and with the classical results of the field we will end up giving some examples where modules have decompositions that satisfy a nice combinatorial condition. As a last step, we hint to a generalisation to the setting of biproduct decompositions in preadditive categories.

Rif. int. C. Marastoni, T. Vargiolu

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