# Ludwig Heldin: Flatness in Commutative Algebra

**Time: **
Wed 2018-12-12 10.00 - 11.00

**Lecturer: **
Ludwig Heldin (BSc student)

**Location: ** Room 14, House 5, Kräftriket, Department of Mathematics, Stockholm University ￼ ￼

Abstract:

*The text is a brief exploration of commutative algebra in the context of using commutative algebra and its mathematical neighbors (category theory, homological algebra, topology) to mainly prove theorems about flatness. It starts with a quick recap of the relevant ring theory and moves on to construct the prime spectrum of a ring. Proving some elementary theorems in the process. Then central concepts like modules and exact sequences are introduced, as well as flatness after introducing the tensor product. After some elementary Theorems on flatness the Tor-functors are constructed and some more advanced proofs are proven with the help of them and direct limits. The end of the paper discusses the role of localization in flatness as well as how flatness relates to the prime spectrum.*