Text: Thomas W. Hungerford, Algebra, Springer Verlag (required).
But I will teach the course from my own classroom notes:
Additional Reading: Finitely
generated torsion-free modules are free. If you drop finitely generated then
this is no longer true. The additive group of rational numbers (Q,+) is a nice example
of a torsion free group which is not free. Another example is provided
by the product of countably many copies of the additive group (Z,+) of
integers. The article
Baer's result: The infinite product of the integers has no basis by Stefan Schroer, University of Düsseldorf, explains
this exceptionally well.
Prerequisites:
Course Description:
The second semester of Modern Algebra will be mainly on modules over principal ideal domains, Sylow theory,
free algebras and sums, ultraproducts.
You will receive weekly homework assignments and there will be a midterm and final.
You also might profit from my notes on
Advanced Linear Algebra. These
notes are based on the classic linear algebra text by K. Hoffman
and R. Kunze. I had prepared these notes about twenty years ago
with a by now defunct word processor. Typesetting is not very good, compared to
LaTeX. For doing the problems you need the Hoffman-Kunze book. which I highly
recommend.