Advanced Algebraic Structures

Faculteit | Science and Engineering |
Jaar | 2022/23 |
Vakcode | WBMA011-05 |
Vaknaam | Advanced Algebraic Structures |
Niveau(s) | bachelor |
Voertaal | Engels |
Periode | semester I b |
ECTS | 5 |
Rooster | rooster.rug.nl |
Uitgebreide vaknaam | Advanced Algebraic Structures | ||||||||||||||||||||||||||||
Leerdoelen | At the end of the course, the student is able to: 1. recognize, analyse, and calculate with examples the abstract notions ‘field extension’, `separability’, `normality’. The Galois correspondence can be formulated, and used in concrete examples. Moreover basic definitions, examples, and applications of the theory of modules over a commutative ring are understood (cyclic modules, Hom's, tensor products, exact sequences). 2. acquire skills in reproducing and designing proofs relevant in this theory. |
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Omschrijving | One half of the course extends the field theory introduced in the course Algebraic Structures. Topics treated include Galois Theory, cyclotomic fields, quadratic reciprocity. The other half of the course treats some basic theory of modules over commutative rings (including tensor products). |
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Uren per week | |||||||||||||||||||||||||||||
Onderwijsvorm | Hoorcollege (LC), Werkcollege (T) | ||||||||||||||||||||||||||||
Toetsvorm |
Schriftelijk tentamen (WE)
(Final mark equals the grade for the final exam.) |
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Vaksoort | bachelor | ||||||||||||||||||||||||||||
Coördinator | Dr. J.S. Müller | ||||||||||||||||||||||||||||
Docent(en) | M.W. Lüdtke, PhD. ,Dr. J.S. Müller | ||||||||||||||||||||||||||||
Verplichte literatuur |
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Entreevoorwaarden | The course unit assumes prior knowledge acquired from Group Theory, Linear Algebra 1 and 2, and Algebraic Structures. | ||||||||||||||||||||||||||||
Opmerkingen | |||||||||||||||||||||||||||||
Opgenomen in |
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