Part 1
Foundations
Chapter 1
Sets and vector spaces
We assume some familiarity with basic notions from set theory and linear
algebra. For example the reader should be comfortable working with nite
dimensional vector spaces over a eld, their bases, and lin
Algebra: Assignment 7
Due on Wednesday, November 21, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 25, 2012
Contents
Exercise 2
Part (a)
Part (b)
Part (c)
.
.
.
.
3
3
3
3
E
Algebra: Assignment 5
Due on Firday, November 2, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 21, 2012
Contents
Exercise 4.4.10
Part (a) . . .
Part (b) . . .
Part (c) . .
Algebra: Assignment 4
Due on Friday, October 26, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 21, 2012
Contents
Exercise 4.1.6 . . . . . . . . . . . . . . . . . . . . . .
Abstract Algebra: Assignment 3
Due on Friday, October 19, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 21, 2012
Contents
Exercise 3.4.2 . . . . . . . . . . . . . . . . . .
Abstract Algebra: Assignment 2
Due on Friday, October 12, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 21, 2012
Contents
Exercise 2.4.5 . . . . . . . . . . . . . . . . . .
Abstract Algebra: Assignment 1
Due on Friday, October 5, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited November 21, 2012
Contents
Exercise 1.2.3 . . . . . . . . . . . . . . . . . .
Sample homework
solutions 1
1.2.3 Let V be a nite dimensional vector space and W V be a subspace. Show that W is nite dimensional and any basis of W can be
extended to a basis of V . Deduce that dim W dim V with equality
if and only if W V .
If W is not n
Modules review
True or False?
1. Let V W X and V W Y be decompositions of a left
R-module V as direct sums of submodules. Then X Y .
2. Let V W X and V W Y be decompositions of a left
R-module V as direct sums of submodules. Then X Y .
3. If V is a simple
Algebra Midterm 1
Fall 2012
Work out if each of the following statements is TRUE or FALSE.
Justify your answer carefully by supplying a PROOF or a COUNTEREXAMPLE.
1. Let Vecf pRq be the category of nite dimensional vector spaces
over R, and D : Vecf pRq V
Algebra: Assignment 8
Due on Wednesday, December 5, 2012
Brundan 1:00pm
A digital copy of this document can be found at http:/pages.uoregon.edu/raies
Dan Raies
Last edited December 6, 2012
Contents
Exercise 4 . . . . . . . . . . . . . . . . . . . . . . .