Algebra 2 06-ZALGLM2

After completing the course a student should know the following topics and have proficiency in their applications:
The second isomorphism theorem for groups.
Free abelian groups (sets of free generators, rank, subgroups).
The structure of the finitely generated abelian groups.
Symmetric groups (normal subgroups of Sn, simplicity of An).
Soluble groups (composition sequences, Jordana-H?lder theorem).
Noetherian rings (the Hilbert basis theorem).
Dedekind domains (uniform factorization into prime ideals).
Divisibility in polynomial rings (Gauss lemma, unique factorization polynomial rings, Eisenstein criterion).
Splitting field of a polynomial (existence and uniqueness).
Algebraic closure of a field (existence and uniqueness).