Universiteit Leiden

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Decompositions in algebra

We show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and consider the ring of algebraic integers as such a lattice.

D.M.H. van Gent
05 March 2024
Thesis in Leiden Repository

We compute some invariants using capacity theory and obtain a partial solution to the (algorithmic) closest vector problem. We generalize the results on (universally) graded rings by Lenstra and Silverberg. We study the special case of group rings, and show that under similar assumptions rings can be uniquely decomposed into a group ring in a maximal way. We give a functorial algorithm to compute roots of fractional ideals of orders in number rings.

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