Rigorous Proof of Frobenius Reduction

Dec 15, 2022
Paper

Abstract

This work is originally from the Homework of the abstract algebra course at Ecole Polytechnique for MAA201-Reduction of Endomorphisms. And I spend this work on this project.

In the first part you can see some rigorous proof of Gauss’s Lemma and Eisenstein’s Criterion, and some application in the analysis of the reducibility of the monic polynomials.

And in the second part, we will see the proof of Frobenius Reduction which in French is Decomposition de Frobenius. Since there is no really detailed proof of this in English so here you can find the Lemma and proof relatively in order to prove this theorem.

Copyright by Yubo Cai

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Yubo Cai 蔡宇博
Yubo Cai 蔡宇博

My research interests include Computational Mathematics, Operation Research, Machine Learning.