FSF3603 Commutative Algebra 2 7.5 credits

• Integral extensions
• Chain conditions: Artinian rings
• Valuation rings
• Completions
• Hilbert functions
• Dimension theory for local rings
• Regular sequences
• Some extra material which can vary depending on the lecturer's choice, e.g.
• The Koszul complex, Hilbert Syzygy theorem
• Cohen-Macaulay
• Descent

After the course, the student should have sufficient depth in the field to be able to continue research in commutative algebra and have a good background in commutative algebra for algebraic geometry.

A Master degree including at least 30 university credits (hp) in in Mathematics (Calculus, Linear algebra, Differential equations).

Basic knowledge in abstract algebra equivalent courses SF2737 Commutative Algebra and Algebraic Geometry and SF2735 Homological Algebra and Algebraic Topology.

M.F. Atiyah and LG. Macdonald, Introduction to Commutative Algebra.

For the extra material: D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, t.ex.

If the course is discontinued, students may request to be examined during the following two academic years.

• INL1 - Assignment, 7.5 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Homework exercises in combination with an oral exanimation.

Accepted home assignments andoral presentation.

Mats Boij

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.