# News

14.08: First lecture Monday 19.8, at 15:15 in F3.

# General information

Lecturer: sverre o. smalø, email: sverresm at math ntnu no, SBII, room 850, tlf. 735 91750

Office hours: Tuesdays 11:00-12:00, SBII, room 850

Teaching hours:

 Lectures: Monday 15:15-17:00, F3, Are moved to K24 from Mondag 16/9 through Monday 21/10-13 Friday 10:15-12:00, F4

Some of the Friday-lectures will be used for exercise sessions.

Meeting in the reference group on Wednesday Sept. 25th at 16:00 in room 850 in SII.

# Textbook and syllabus

Textbook

 Authors: P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul Title: Basic Abstract Algebra Publisher: Cambridge University Press Edition: Second Edition ISBN: 0-521-46629-6

Preliminary syllabus:

 Chapter 9 All sections Chapter 10 All sections Chapter 14 14.1-14.5 Chapter 19 19.1-19.3 Chapter 20 All sections Chapter 21 All sections

# Plan/log

Date Themes Reference
19.08 Introduction, definitions, various examples Chap 9.1, 9.2, 9.3
23.08 Polynomial rings and formal power series, subrings, characteristic of a ring, algebras, ideas and homomorphisms Chap 9.4, 9.5, 10.1, 10.2
26.08 More on Ideals and homomorphisms, left ideals, right ideals, ideals in the full matrix algebra, sums and direct sums of ideals, products of rings, Chap 10.1, 10.2, 10.3
30.08 Minimal, maximal and prime ideals, the real numbers as the rings of Cauchy-sequences modulo the ideal of sequences converging to zeroChap 10.4
02.09 Maximal ideals are prime, the maximal ideals of Z, C[x] and R[X], description of prime ideals for commutative rings. Nilpotent and nil ideals, Zorns's lemma and the existence of maximal ideals.Chap 10.5,10.6
06.09 Modules and VectorspacesChap 14.1, 14.2
09.09 The rest of Chapter 14.2, and most of 14.3Chap 14.2, 14.3
09.13 Some exercises, the rest of 14.3 and started on 14.4Chap 14.3, 14.4
09.16Rest of 14.4 and started on 14.5Chap 14.4, 14.5
09.20Finished 14.4 started on 19.2 Chap 14.5, 19.2
09.23Finished therem 19.2.5 and 19.2.6, gave examples, and finished section 19.1 Chap 19.1, 19.2
09.27We will take a look at the exercises, so look through the exercises given as exercise 1, 2 and 3, and make and efford to try to solve those problems
09.30Endomorphism ring of a direct sum as a matrix ring, Th 19.2.7, 19.2.8,19.2.9, 19.2.10Chap 19.1, 19.2
10.04Exercise 2 and 3
10.07Th 19.2.11, 19.2.12, 19.2.14, Examples 2.15 a, and b. Chap 19.2
10.11Exercise 4 and 5
10.14Wedderburn Artin theoremChap 19.3
10.18Exercise 5 and 6
10.21Comments on Weddernburn Artin theorem and start on Smith normal form Chapter 20.1
10.25Exercise 6 and 7
10.28 Smith normal form Chapter 20.1

# Exam

Final exam: 18.12.2013, written, 4 hours, 15:00-19:00

# Problem sessions

 Exercise 1 Chapter 9, page 173-176: 1, 2, 3, 4, 5, 7, 9, 11 Chapter 10, page 187: 1, 2, 4, 7 Exercise 2 Chapter 10, page 194-195: 1, 2, 3, 4, 8, 10, 11, 12 page 202-203: 1, 2, 3, 4, 7 Exercise 3 Chapter 10, page 209: 1, 2, 4, 6 page 210: 1, 2 Exercise 4 Chapter 14, page 252-253: 1, 3, 4, 5, 8, 10, 11 page 260: 2, 3, 4, 6, 7 Exercise 5 Chapter 14, page 262-263: 1, 2, 3, 5, 6 page 268: 1, 2, 4, 5, 7, 8, 9 Exercise 6 Chapter 19, page 368: 1, 2 page 381: 1, 4, 6 Exercise 7 Chapter 19, page 381-382 2, 7, 8, 9, 11 Exercise 8 Chapter 19, page 388 3, 5 chapter 20, page 401 1,2,3 Exercise 9 Exam Dec 11 2007 Problems 1, 2, 3 Nov 30 2005 Problems 1, 4 Exercise 10 Dec 11 2007 Problem 4 Nov 30 2005 Problem 2, 3 Dec 11 2009 Problem 2, 3 Exercise 11 Dec 13 2010