Instructor

Prof. Michael Larsen
Rawles Hall 303
Tel. 1-812-855-1064
E-mail mjlarsen@indiana.edu
Office hours to be announced.

Textbook

Abstract Algebra, Third Edition, by Dummit and Foote

Homework

• Due January 24
  • 10.4: 1, 6, 11, 13, 15, 24, 27
  • 10.5: 3, 5, 7, 9, 22
  • Prove the snake lemma.
• Due February 7
  • 10.3: 24
  • 10.5: 14, 20
  • 11.2: 9, 11, 39
  • Prove that the symmetric and exterior squares of an n-dimensional vector space V have dimension (n²+n)/2 and (n²-n)/2 respectively.
  • If a linear transformation T from an n-dimensional vector space V to itself is diagonalizable with eigenvalues λ_i, what are the eigenvalues of the tensor product of T with itself acting on the tensor square of V?
  • Given a short exact sequence of modules over a commutative ring, prove that the middle term is finitely generated if the other two terms are.
  • If B is a flat A-algebra and N is a flat B-module, prove that N is a flat A-module.
• Due February 21
  • 11.3: 2, 3
  • 12.1: 3, 6, 9, 21
  • 12.2: 4, 11
  • 12.3: 12, 17, 34
  • 13.1: 3, 4, 5
• Due March 7
  • 13.2: 4, 5, 9, 14, 19, 22
  • 13.4: 3, 5, 6
  • 14.1: 7, 9
• Due March 28
  • 14.2: 5, 13, 14
  • 14.7: 2, 3, 16
  • It is an easy theorem in group theory that every non-trivial group of prime power order has non-trivial center. Deduce that every group of prime power order is solvable.
• Due April 18
  • 15.1: 4, 10, 18, 21
  • 15.2: 2, 6, 21, 22, 27
  • 15.3: 5, 8, 15