Algebra I

Course content

Groups quotient groups, isomorphism theorems, alternating and dihedral groups, direct products, free groups, generators and relations, free abelian groups, actions. Sylow theorems, nilpotent and solvable groups, normal and subnormal series. Rings, ring homomorphisms, ideals, factorization in commutative rings, rings of quotients, localization, principle ideal domains, Eucladian domains, unique factorization domains, polynomials and formal power series, factorization in polynomial rings.