Abstract Algebra II

22m121, Spring 2005

Instructor: Fred Goodman


Review sheet for first test.

Review sheet for second test.

Review sheet on fields for the final.

Errata sheet for Goodman, Algebra

Correct link to purchase Herstein, Topics in Algebra at discount: Abebooks .

Reserve list in Math Library:

Herstein, Topics in Algebra (2 copies)

Vinberg, A Course in Algebra.

Jacobson, Basic Algebra I (1985)

Jacobson, Lectures in Abstract Algebra, Vol II (Linear Algebra)

Improved text for section 2.7.

Revised section 3.4 and new section 3.5. (revised Saturday, March 19; added some comments on similar matrices and similar transformations)

Improved text for sections 6.1 through 6.3.

Improved text for section 6.6.

New sections M.1-M.2 (modules, version of Monday Feb. 21)

New section M3 (determinants, version of Monday Feb 28, needs proofreading.)

New sections M4-M5 (version of Saturday, March 19. complete, but needs exercises. Removed superfluous section M6 with a second proof of structure theorem for finitely generated torsion modules over a PID).

New section M6 (Version of Saturday, March 26, with subsection on characteristic and minimal polynomials)

Program for diagonalizing integer or polynomial matrices, and examples of canonical form computations.



Contact Information:


325G Maclean Hall


goodman at math dot uiowa dot edu


Office: 319-335-0791

Paper Mail:

Fred Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242-1419 USA

Office Hours:

MW 1:30-2:20

Teaching Assistant:

Oscar Vega

Office hours: TBA



Click here

Problem session:

12:30P - 1:20P T 116 MH


See note on textbooks in the course syllabus.

Frederick M. Goodman, Algebra: Abstract and Concrete, 2nd edition, Prentice Hall, 2002.

This text is required.

I. N. Herstein, Topics in Algebra, 2nd edition

This text is recommended.

Assignment lists:

There will be 8 to 12 written assignments. Details will appear here as the assignments are made.Please see the remarks on the syllabus about the standard of explanation expected on the homework.

First assignment, Due Friday, Jan. 28:

Section 6.1, Exercises: 8, 15.

Section 6.2, Exercises from the revised text: 2, 10-15, 22.

2nd assignment, Due Friday, Feb. 4:

Section 6.3, Exercises from the revised text: 2, 3, 8, 9, 11

Section 6.4, Exercises 1, 2

3rd assignment, Due Friday, Feb. 11:

Section 6.5, Exercises 5, 7, 10, 11, 12, 23, 24.

Section 6.6, Exercises 3, 4, 5. Note: for exercise 5, the correct statement is that R does not satisfy the ACC for principal ideals, but every irreducible is prime.

4th assignment, Due Friday, Feb. 18:

Section 6.8, Exercises 4, 5, 6.

5th assignment, Due Monday, Feb. 28:

Section 3.5, Exercises 3, 4, 11, 12.

Let B and C be two ordered bases of a finite dimensional vector space V. Let T be an element of End_K(V). Show that there is an invertible matrix S such that (the matrix of T with respect to C) = S (matrix of T with respect to B) S^{-1}.

6th assignment, Due Friday, March 4:

Section M1, Exercises 3, 5, 8, 9,10.

7th assignment, Due Friday, March 11:

Section M2, Exercises 4 and 7

Section M3, Exercises 1, 2, 3, 4, 6

8th assignment, Due Friday, March 25:

Characteristic polynomials and triangular form.

9th assignment, Due Friday, April 1 (ha!):

Exercises on modules.

10th assignment, Due Friday, April 8 :

Oscar's assignment

11th assignment, Due Monday, April 25 :

Section 7.3 Exercises 5, 6, 7, 10.

Section 8.1 Exercises 1-3.

Section 8.2 1, 3.



There will be two midterm exams, dates to be negotiated; the dates will appear here when they are known. There will be a comprehensive final exam. The text of the exams will appear here after the exams have been done by all students.

Exam 1, text

Exam 2, text