This is a collection of exercises corresponding to the lecture Algebra II held by Prof. G. Kemper at the Technical University Munich in the summer semester 2020, based on the book A Course in Commutative Algebra.
Topics covered include:
- Hilbert’s Nullstellensatz
- Noetherian and Artinian rings
- the Zariski topology on affine varieties and the spectrum of rings
- Krull dimensions
- localizations
- Nakayama’s lemma and the principal ideal theorem
- integral extensions