Mathematics 893 Problem Set 1

Text: Abstract Algebra, Third Edition, by Dummit and Foote

Suggested reading: The Preliminaries (pages 1-12) are assumed as background for the course. You should look this section over to see what is there, and use it as reference when necessary. Then read sections 1.1 and 1.2.

Questions due next Friday (September 23): Page 21: 6, 7, 11, 19, 20, 21, 22, 23, 32, 36.

If you have not seen groups before, in particular if you have not seen ℤ/nℤ, then you should study carefully pages 8-11 and try a few of the introductory exercises (e.g. 5-12 on page 11, and 1-4 on page 21).

Notation: I will use the notation of the text for the most part. (Much of the basic notation is introduced in the Preliminaries.) However I prefer other notation in a few cases. I will use A\B for the difference set

A\B = {a|a ∈ A, a ∉ B}

instead of A−B, and I will use gcd(a, b) instead of (a, b) for the greatest common divisor of two integers a and b. The reason for this is that A − B and (a, b) often mean other things, e.g. A − B sometimes means {a − b|a ∈ A, b ∈ B} and (a, b) could be just a row vector.