Algorithmische Algebra: Wintersemester 2018/19

✍ Scribed by Mohamed Barakat

• Year: 2019
• Tongue: German, English
• Leaves: 101
• Series: Lecture notes
• Edition: version 2019-01-31
• Category: Library

✦ Table of Contents

Gruppen
Operationen
Definition Gruppe, symmetrische Gruppen
Untergruppen, Erzeugung, Homomorphie
Freie Gruppen
Definition Operation, Bahnenalgorithmus
Nebenklassen und der Satz von Hölder
Stabilisatoren
Klassifikation transitiver Operationen
Erzeuger für Stabilisatoren
Beispiel von Operationen und Untergruppen, Anwendungen
Die Konjugationsoperation
Anwendung auf kombinatorische Abzählprobleme
Homomorphiesatz
Stabilisatorketten
Die Sylowschen Sätze
Gröbner bases
Monomials and monomial ideals
Monomial orderings
Division with remainder
Gröbner bases and Buchberger's algorithm
First applications: Submodule membership and syzygies
Iterated syzygies and Hilbert's Syzygy Theorem
Elimination
Constructive Abelian categories
Categories
The category of modules
Objects
Morphisms
Subobjects and factor objects
Kernels and cokernels, images and co-images
Products and coproducts
Pull-backs and push-outs as kernels and cokernels
More categorical notions
Additive and Abelian categories
Computable rings
A constructively Abelian category of matrices
Functors
Natural transformations
Exact sequences, homology, and cohomology
Free resolutions