Algebra I Autumn 2026

Lecturer
Rahul Pandharipande
Coordinator
Lycka Drakengren

Exercise classes

The exercise classes start in the second week of the semester.
TimeRoomAssistant
We 16-18HG D 7.1Persian Tursunov
We 16-18LFW B 1Kyran Stoecklin
We 16-18LFW C 4Pacifico Rodriguez
We 16-18LFW E 13Andres Lopez Gutierrez
We 16-18RZ F 21Marvin Ernst

Literature

The main reference for the course is J. Rotman, "Advanced modern algebra, 3rd edition, part 1" (link only works from ETH computers and via vpn).
Below we give page references from this book for each week of the course.

We can also recommend the following two books for the course: For more literature as well as more information about the course, please see the VVZ page here. Review on groups, rings and fields

Links

Public lectures by Rahul Pandharipande: ICM 2018 Hirzebruch Lecture, 2023

The new exercises will be posted here. We expect you to look at the problems over the weekend and to prepare questions for the exercise classes on Wednesday.

Please hand in your solutions online by the following Friday at 12:00 at the following link. Your solutions will usually be corrected and before the following exercise class. On every Friday (6:00 - 00:00) there will be a quiz, which should be attempted and handed in digitally and individually at the following link. No use of books, notes, people or internet searches are permitted.

Links to polyboxes of TA's: Andres Lopez Marvin Ernst Pacifico Rodriguez Kyran Stoecklin

Information about quizzes: For 10 or more passed quizzes, there is a grade bonus of 0.25 grade points. For fewer passed quizzes, the bonus is proportional. The bonus is added to the unrounded grade from the exam; the result is rounded to the final grade.

week material covered (page numbers: see main reference) assignment due by solutions
1 General information on the course, arithmetic with the integers, Zorn's lemma. (pages 9-13, 313-314, 319-320) A1 Sept 25 S1
2 Category Theory, first definitions on Rings (pages 441-445, 461, 29-37); see also fields summary A2 Oct 2 S2
3 Fraction field, Polynomial Rings (pages 36-38, 41-45, 48-49) A3 Oct 9 S3
4 Ideals, First Isomorphism Theorem (pages 50-51, 55-60, 61: Ex A-3.52, 21: A-2.25, 74-75) A4 Oct 16
5 Prime ideals and maximal ideals, Existence of maximal ideals, Arithmetic of Polynomials with coefficients in a field, Chinese Remainder Theorem, definition of UFD (pages 74-75, 315, 62-64, 104)