Algebra III - rings and fields
Résumé de section
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Lecture title: Algebra III - rings and fields
Course materials:- Instructor: Leonid Monin
- Assistants: Léo Navarro Chafloque, Paul Vögele, Yang Zhang
- Lectures: Mondays 13-15 in CM 4
- Exercises: Wednesdays 15-17 in CM 1105
Lectures will be in english and problem sheets in french.
The main source for this course is the following lecture notes. The file might be updated throughout the course, so we recommend to check for the new versions regurarly.
Additionally, the videos of the 2020–21 lectures given by Zsolt Patakfalvi can be found here. But be aware that topics this year could be slightly different.
Finally, if you need additional sources, you can consult the following books. The course does not follow these books:
- Michael Artin: Algebra
- Joseph J. Rotman: Advanced modern algebra
Final grade:
The final grade will be calculated from the final exam. This means that if you obtain at least of the points on the exam, you will receive at least a 4 as your final grade.
Unfortunately, there will be no bonus exercises this semester because of ChatGPT.
Ed-discussion:
In the “General Information” section of this page you will find the link to the course Ed discussion forum: https://edstem.org/eu/courses/3109/discussion
We will respond on Ed discussion only to questions about the course material. If there is a suggestion or question about the course organization, it must be communicated through the course representative.
Advice :
It is very important to follow the course and the exercise sessions continuously. We recommend rereading the material from the previous lecture before each class, and also solving the exercises.
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Edit: (17.02 17h20) J'ai enlevé des points mentionnant les anneaux de groupes, notion pas encore vue.
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Edit (24.02) : ajout d'une partie de solution manquante pour l'exo 4.1
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Ajouté une solution pour les derniers points du premier exercice (edit: 11.03)
Ajouté une remarque de contexte (edit: 07.04)
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Edit (04.04): précision quant à la définition de morphisme de $A$-algèbres pour l'exercice 4.
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Edit (17:30, 15.04) Changé l'exercice 3, la version précédente n'allait pas sur plusieurs points.
Edit bis (18.04): Changé la constante du dernier point de l'exo 3, pour rendre la remarque plus pertinente
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You could find the recording of the lecture here.
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Exam Structure
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Theoretical exercises: These will be based on propositions, definitions, examples, and proofs from the course. Everything asked here is contained in the LaTeX course notes. The questions may be slightly adapted to make them suitable for an exam. For example, a question could be a specific part of a course theorem or a combination of different examples and statements from the notes. Other adaptations are also possible.
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Exercise sets: You can find solutions to these in the Moodle answer keys. We may slightly adapt these questions compared to their original versions in the exercise sets. Supplementary exercises are excluded.
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New exercises: These questions cover the content of the course and exercise sessions but will not have previously appeared in the notes or exercise sets.
- Language: The exam questions will be given in both english and french.
Exam Rules and Logistics
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Cheat sheet: You may use one A4 handwritten cheat sheet (written by yourself, double-sided is allowed) during the exam.
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Permitted materials: You may bring your cheat sheet, food, writing materials, and your Camipro card. We will provide scratch paper. You must hand in your cheat sheet at the end of the exam.
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Using course results: You may use any results seen in class or in the exercises, unless the question specifically asks you to prove that exact result or an obvious special case of it. When using a course result, you must either cite it by its name or cite the proposition precisely by stating: "We saw in class that [insert the statement]."
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