250026 VO Algebraic structures (2012W)

This lecture will give an introduction to abstract algebra. We will cover the following objects and their properties pertaining to group theory: normal subgroups and quotient groups, isomorphism theorems, Lagrange's theorem, cyclic groups, products of groups, permutation groups. We will cover the following objects and their properties pertaining to ring theory: characteristic and prime rings, ideals and factor rings, isomorphism theorems, direct sums and direct products, polynomial rings, principal ideal domains, euclidean rings, chinese remainder theorem for rings, integral domains and quotient fields, unique factorization domains, irreducibility criteria. For more information (in German) go to http://www.mat.univie.ac.at/~baxa/ws1213.html