Course: Algebraic Structures
Program:

 Rings.
 Polynomial rings.
 Ideals.
 Quotient rings.
 (Homo)morphisms [of rings].
 Field of fractions of an integral domain.
 Euclidian domains.
 Irreducibility of polynomials.
 Groups.
 Permutation groups.
 Matrix groups.
 Abelian groups.
 (Homo)morphisms [of groups] and quotient groups.
 Group actions.

 Fields and Field extensions.
 Algebraic number fields.
 Finite fields.
 Characteristic of a field.
 Constructions by ruler and compass.
 Galois Theory.
 Examples of low degree.
 Resolution of polynomials equations of degree 3 and 4 in one variable.
 Solvable groups, resolution by radicals.
 Examples of equations that cannot be solved by radicals.
Bibliography that is free (or at least open access):
 Michael Janssen and Melissa Lindsey:
ringswithinquiry.org
 Margaret L. Morrow:
Introductory Abstract Algebra, available at jiblm.org
 Tom Judson:
Abstract Algebra: Theory and Applications.
Spanish translation by Antonio Behn,
SAGE exercises by Robert Beezer.
Everything you wanted to know about abstract algebra,
but were afraid to buy!
Available in many formats at abstract.ups.edu
 Frederick M. Goodman:
Algebra: Abstract and Concrete, edition 2.6 (May 1, 2014), 576 pages. Available at homepage.divms.uiowa.edu/~goodman
 Edwin H. Connell:
Elements of Abstract and Linear Algebra,
(March 20, 2004), 138 pages. Available at math.miami.edu/~ec
 James S. Milne:
Group Theory.
v 3.15 (2020), 135 pages.
Available at www.jmilne.org/math
 James S. Milne:
Fields and Galois Theory.
v 4.61 (2020), 138 pages.
Available at www.jmilne.org/math
 Victor Shoup:
A Computational Introduction to Number Theory and Algebra, available at shout.net/ntb under Creative Commons license.
 Emil Artin:
Galois Theory: Lectures Delivered at the University of Notre Dame, 1971, open access