Commutative algebra shows how geometric and number theoretical ideas can be interpreted by means of algebraic structures. Students will study Noetherian and Aritinian rings and modules over such rings. The course topics are dimensions of rings and modules, localisation, tensor products, primary decomposition, and integral extensions.

After completed course, the students shall be able to:

• Define basic concepts and constructions in commutative algebra, as ideals of various sorts, modules, exact sequences, tensor products, localization, primary decompositions, Artinian and Noethian rings, Gröbner bases, filtrated and gradient modules and rings, dimensions of rings and Hilbert series of local and gradient rings.
• Perform simple specific calculations in number rings, polynomial rings and locations of polynomial rings.
• Reproduce the basic results concerning the concepts and constructions above.
• Explain the main ideas in the proofs of these results.
• Use the results in commutative algebra to perform simple reasoning to show properties of rings and modules.

Oral examination.

From the Autumn of 2007: Exam only once a year - Autumn.