Krull-Schmidt-Remak Theorem, Direct-Sum Decompositions, and G-groups

Room 1.22, Mathematics building, FCUP
Friday, 24 March, 2017 (All day)

We will begin by presenting some history of the Krull-Schmidt-Remak Theorem. From groups, we will pass to modules over a ring R, introducing some direct-sum decompositions that follow a special pattern. We will consider invariants that also appear in factorisation of polynomials. Then we will go back from (right) R-modules to groups. Here the category that appears in a natural way is that of G-groups, which substitutes the category of right R-modules. In this category, Remak's result has a natural interpretation.


Alberto Facchini


Università degli studi di Padova

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