MATH 571: Higher Algebra 2
Winter 2011
Course description


Fritz Hörmann
Office ours:Wednesday 11-12, Thursday 11-12
Tel:(514) 398-2998

Course information

Time:Monday, Wednesday, Friday 9:35 AM - 10:25 AM
Location:Burnside Hall 1234
Dates:Jan 04, 2011 - Apr 08, 2011

There will be a mid-term and final exam, as well as weekly exercises. The final grading will be based on the exercises (20 %), mid-term exam (20 %) and final exam (60 %).


Hand in onExerciseSolutions
Mon, Jan 17Assignment 1 
Mon, Jan 24Assignment 2 
Mon, Feb 7Assignment 3 
Mon, Feb 14Assignment 4 
Fri, Mar 4Midterm Exam 
Mon, Mar 14Assignment 5 
Mon, Mar 21Assignment 6 
Fri, Apr 1Assignment 7 

Exercises are usually to be handed in on Mondays.



  1. Dommit, David S; Foote, Richard M.; Abstract Algebra. Wiley; 3 edition (July 14, 2003), 944 pp., ISBN: 978-0471433347
...on reserve in Schulich Library.


  1. Eisenbud, David; Commutative Algebra with a View Toward Algebraic Geometry Springer-Verlag, New York, 1995, ISBN: 978-0387942698
  2. Lang, Serge; Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002. xvi+914 pp. ISBN: 0-387-95385-X
  3. Jacobson, Nathan; Basic algebra. II. Second edition. W. H. Freeman and Company, New York, 1989. xviii+686 pp. ISBN: 0-7167-1933-9
  4. Atiyah, M. F.; Macdonald, I. G.; Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp.


Rings, Part I.

  1. Integral extensions and the going-up and going-down theorems.
  2. Noether's normalization lemma, and Hilbert's Nullstellensatz.
  3. Noetherian and Artinian rings.
  4. Hilbert's basis theorem.

Modules, Part II.

  1. Tensor products.
  2. Projektive modules.
  3. Injective modules.
  4. Flat modules.

Rings, Part II.

  1. The Jacobson radical.
  2. Nakayama's lemma.
  3. Semisimple rings and modules.
  4. Jacobson's density theorem and the Artin-Wedderburn theorem.

Categories, Part III.

  1. Exact functors.
  2. Adjoint functors.

Groups, Part II.

  1. Linear representations of groups.
  2. Maschke's theorem.
  3. Characters. Orthogonality of characters. Frobenius Reciprocity.
  4. Representations of nilpotent groups.
  5. Representations of the symmetric group.
  6. Representations of GL_2(F), for F a finite field.

- if time is left - Homological algebra.

  1. The snake lemma and the 5 term lemma.
  2. Projective and injective resolutions and derived functors.
  3. The derived functors Tor and Ext.
  4. Homotopy and independence on the resolution.


McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offenses under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).