"Advanced Algebra (for PhD students)" and "Selected Topics in Algebra" - Commutative Rings

Begin: Thu March 3, 12:15-13:45 in the new seminar room SR NT02008, Kopernikusgasse 24, 2nd floor. So far, we have reserved the room for Thu and Mon 12-14, but the times are flexible: we will discuss possible times at the first lecture March 3. If you are interested but not able to make it Thu March 3 at 12:15, send email.

The subject of the course is the theory of commutative rings, with emphasis on valuations and those classes of rings that can be defined using valuations: Dedekind domains, Prüfer rings, Krull rings.

The course supplies fundamental prerequisites for algebraic number theory (Dedekind domains) and for algebraic geometry (Hilbert's Nullstellensatz). Also included in this course is a brief introduction to point-set topology. I will supply typed course notes in English.

Connections to Topological Methods in Commutative Algebra: This course also supplies the prerequisites for a course in Fall 2016/17 "Topological Methods in Commutative Algebra" by Carmelo Finocchiaro, one of the foremost experts on this topic. His course is highly recommended for anybody interested in algebra and/or topology.

Notes in progress

Commutative Ring Theory Notes

Sophie Frisch