7.5 credits cr.
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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.
The course consists of one module.
Instruction consists of lectures and exercises.
The course is assessed through written examination.
A list of examiners can be found on
ScheduleThe 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.
Note that the course literature can be changed up to two months before the start of the course.
During your studies
You can find our course webpages on kurser.math.su.se.