Norsk
Course MAT220

# Algebra

## Course offered:

### Course offered by

 Number of credits 10 Course offered (semester) Spring Schedule Schedule Reading list Reading list

English

None

### Learning Outcomes

After completed course, the students shall be able to:

• Do basic arguments with groups, rings, and fields.
• Give definitions and notions related to groups, rings, fields, and homomorphisms
and isomorphisms of these. In particular permutations, group actions, factor groups
and factor rings, integral domains, quotient fields, polynomial rings, ideals, prime ideals,
maximal ideals, and field extensions.
• Perform basic calculations involving the above mentioned notions, both in concrete
cases and in more general and abstract cases.
• Describe the main ideas in proofs involving the notions above, like for instance the
impossibility of trisecting the angle and doubling the cube.

Spring

English

### Aim and Content

The course covers basic theory of groups and permutations, normal subgroups, group homeomorphisms and factor groups, group actions and Sylow Theory. In addition, the course includes the basic theory of rings and fields, polynomial rings, ideals and factor rings. Studies also include field extensions, finite fields and unique factorisation domains. In the latter, the focus is on groups of utomorphisms of fields, including the Galois theory necessary to show the insolvability of the general quintic by radicals.

### Learning Outcomes

After completed course, the students shall be able to:

• Do basic arguments with groups, rings, and fields.
• Give definitions and notions related to groups, rings, fields, and homomorphisms
and isomorphisms of these. In particular permutations, group actions, factor groups
and factor rings, integral domains, quotient fields, polynomial rings, ideals, prime ideals,
maximal ideals, and field extensions.
• Perform basic calculations involving the above mentioned notions, both in concrete
cases and in more general and abstract cases.
• Describe the main ideas in proofs involving the notions above, like for instance the
impossibility of trisecting the angle and doubling the cube.

None

### Recommended previous knowledge

MAT121 Linear Algebra

### Assessment methods

Written examination: 5 hours