# Advanced algebra
**Source**: https://www.su.se/english/education/course-catalogue/mm/mm7033?semester=HT2026&eventcode=48116
**Parent**: https://www.su.se/english/education/course-catalogue?q=&internationalStudents=%5B%22true%22%5D&forcedReasonCode=%5B%220%22%5D
The course covers fundamental algebraic structures och theorems that provide a foundation for more advanced algrebraic studies, e.g., in algebraic geometry.
In particular, the following is covered.
Field theory: Splitting fields, minimal polynomials. Finite fields. Zorn's Lemma. Existence of algebraic closure and transcendental bases. Existence of maximal ideals in rings.
Module theory: Submodules and quotient modules, direct sums and products, free modules, isomorphism theorems. Finiteness conditions. Short exact sequences. Tensor products. Localization. Universal properties. Multilinear algebra. General definitions of trace and determinant. Noetherian rings and modules. The Hilbert basis theorem.
Applications: An assortment of applications within commutative algebra, representation theory, algebraic geometry and category theory.
## [Course structure](#svid10_142dc5821901009a5b52688b)
The course consists of one module.
### Teaching Format
Instruction consists of lectures and exercises.
### Assessment
The course is assessed through written examination.
#### Examiner
A list of examiners can be found on
[Exam information](https://su.se/math/exams)
## [Schedule](#svid10_142dc5821901009a5b5268da)
The schedule will be available no later than one month before the start of the course.
We do not recommend print-outs as changes can occur. At the start of the course,
your department will advise where you can find your schedule during the course.
- [Schedule MM7033 Autumn semester 2026 Day-time 25%](https://cloud.timeedit.net/su/web/stud1/s.html?sid=3&type=courseevent&h=t&object=cevt_48116_HT2026&startdate=20260801&enddate=20270416&l=en&h2=2 "Link to schedule - opens in new window")
## [Course literature](#svid10_142dc5821901009a5b5268f0)
Note that the course literature can be changed up to two months before the start of the course.
Antoine Chambert-Loir: (Mostly) commutative algebra, Universitext, Springer.
[List of course literature Department of Mathematics](https://su.se/math/courseliterature)
## [Course reports](#svid10_142dc5821901009a5b5268f2)
Course reports are displayed for the three most recent course instances.
[Course evaluations and course reports can be found on the archive page](https://kurser.math.su.se/course/view.php?id=1475)
## [More information](#svid10_142dc5821901009a5b526901)
[New student](https://www.su.se/department-of-mathematics/education/new-student)\
[During your studies](https://www.su.se/department-of-mathematics/education/during-your-studies)
### Course web
You can find our course webpages on [kurser.math.su.se](https://kurser.math.su.se/).
## [Contact](#svid10_142dc5821901009a5b52690b)
[Student contact at the Department of Mathematics](https://www.su.se/department-of-mathematics/education/contact)
Find more courses and programmes
Know what you want to study?
[Find your study programme](https://www.su.se/english/education/course-catalogue)
What can I study?
[Explore our subjects](https://www.su.se/english/education/course-catalogue/education-subjects)
## Autumn 2026 | Period 1 | Day-time, 25% | On campus | For international students
7.5 credits
Autumn 2026
Period 1Day-time, 25%On campusFor international students
Beginning/EndPlease view course schedule for exact dates
week commencing
30/08/2026 - 16/01/2027
Held every autumn
Apply
Application deadline 14 April 2026
Course code: MM7033
Application code: SU-48116
Level
Master's level
Language
English
Eligibility
For admission to the course, knowledge is required equivalent to Mathematics III - Abstract Algebra, 7.5 credits (MM5020).
Also required is knowledge equivalent to Swedish upper secondary course English 6.
Selection
No selection.
[Syllabus - legal document](#)
Tuition fee
Applies to citizens from outside EU, EEA or Switzerland. First instalment: 17500 SEK. The complete course: 17500 SEK.
[More information on tuition fees](https://www.su.se/english/education/how-to-apply/costs-fees-and-scholarships)
Subject
[Mathematics](https://www.su.se/english/education/course-catalogue/education-subjects/science-and-mathematics/mathematics)
Area of interest
[Science and Mathematics](https://www.su.se/english/education/course-catalogue/education-subjects/science-and-mathematics)
Department responsible for education
[Department of Mathematics](http://www.math.su.se)
Find more courses and programmes
Know what you want to study?
[Find your study programme](https://www.su.se/english/education/course-catalogue)
What can I study?
[Explore our subjects](https://www.su.se/english/education/course-catalogue/education-subjects)