Abstract algebra II combines many of the principles learned in earlier stages of mathematics. Matrices, polynomials, vector spaces, modular arithmetic and more are classified into theoretical ideas with group theory and set theory called algebraic structures. Abstract Algebra gives us the ability to gain new insights into other subjects. In this course, which is a continuation of Abstract Algebra I, the concepts of rings, ideals and isomorphism theorems will be discussed, the ability to use these algebraic structures effectively will be gained and the relationship of abstract algebra with other areas of mathematics will be established.

Rings, integral domains, matrix rings over a field, endomorphism rings, ideals, ring homomorphisms and isomorphism theorems, factorization in rings, polynomial rings, principal ideal domains, unique factorization domains, local rings.