Algebraic structures II

In this course, the student's knowledge of groups, rings and fields is deepened. One way to get a grasp of complicated algebraic structures is to break them down into simple parts. For example it is proven that every finite abelian group is a direct product of cyclic subgroups. Moreover, in ring theory, the concept of unique factorization, which holds in the ring of integers (due to the fundamental theorem of arithmetics), is generalized to more general rings. Finally, the problem of solving polynomial equations motivates the study of field extensions.