562418 PS Introductory seminar to selected topics in Algebra (2005S)

The theory of modules (i.e. "vector spaces" over arbitrary rings) plays a significant role in mathematics and mathematical physics. The first part of these lectures gives an introduction into the basic notions and results of this theory. Then we treat Noetherian modules and give a detailed study of modules over principal ideal domains resp. polynomial rings.The second part
deals with semisimple and Artinian rings and modules. Specific notions as projective (injective) modules, or, e.g. Frobenius algebras are discussed as well as examples from various fields.