Course MAT224
Commutative Algebra
Course offered :
- Current semester
- Next semester
Current programmes of study
Course offered by
| Number of credits | 10 |
| Course offered (semester) | Autumn |
| Schedule | Schedule |
| Reading list | Reading list |
Language of Instruction
English
Pre-requirements
None
Learning Outcomes
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.
Contact Information
advice@mi.uib.no
Course offered (semester)
Autumn
Language of Instruction
English
Aim and Content
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.
Learning Outcomes
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.
Pre-requirements
None
Recommended previous knowledge
MAT220 Algebra
Assessment methods
Oral examination.
From the Autumn of 2007: Exam only once a year - Autumn.
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Contact Information
advice@mi.uib.no