# Algebra I Autumn 2017

Lecturer
Prof. Dr. Emmanuel Kowalski
Organizer
Riccardo Ferrario
Lectures
Wed 13-15 - HG E 5
Fri 08-10 - HG E 5
Exercise session
Mon 14-16 or Wed 15-17 - rooms: see below

This is the webpage of an older Algebra I course. You may want to visit the HS18 Algebra I course webpage

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). For more literature as well as more information about the course, please see the VVZ page here.

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

You are warmly encouraged to hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J 68. Your solutions will be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J 68.

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 29 S1
2 Category Theory, first definitions on Rings (pages 441-445, 461, 29-37) A2 Oct 6 S2
3 Fraction field, Polynomial Rings (pages 36-38, 41-45, 48-49) A3 Oct 13 S3
4 Ideals, First Isomorphism Theorem (pages 50-51, 55-60, 61: Ex A-3.52, 21: A-2.25, 74-75) A4 Oct 20 S4
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) A5 Oct 27 S5
6 UFDs (pages 104-111) A6 Nov 3 S6
7 First definitions on Groups, Group homomorphisms, Subgroups, Conjugacy (pages 127-134, 150-155, 143-145) A7 Nov 10 S7
8 Normal subgroups, quotient groups, Isomorphism theorems for groups (pages ...) A8 Nov 17 S8
9 Group action (see notes), Sylow theorems A9 Nov 24 S9
10 Sylow theorems (continuation, see notes from last week), the symmetric group (pages 116-126, 174-176) A10 Dec 1 S10
11 Field extensions, algebraic elements A11 Dec 8 S11
12 Algebraic closure, splitting field, finite fields A12 Dec 15 S12
13 Finite fields, modules over a ring A13 No hand-in. S13
14 Elementary divisors, Finitely generated modules over a PID A14 No hand-in. S14

All exercise classes are held in English. Please enroll in one exercise group through this link.

timeroomassistant
Mo 14-16LFW C 4Patricia Dietzsch
Mo 14-16ML F 39Carlos De la Cruz Mengual
Mo 14-16ML J 37.1Angela Maennel
We 15-17HG G 19.2 Riccardo Ferrario
We 15-17LEE C 114Alexey Pokrovskiy