Advanced algebra

About this programme

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. To follow your passion. To be close to international career opportunities. To explore city and countryside. In Stockholm you can really get the best of both worlds. Here we explain all the different steps you need to go through when applying to a course or programme. Stockholm University arranges regular webinars and participates in educational fairs and events virtually and around the world to meet students and inform them about our study programmes. Every year Stockholm University welcomes thousands of international students from all over the world. Each bringing their own backpack full of experiences, expectations and dreams. Education and research are closely linked at Stockholm University. As a student, you will have direct contact with leading researchers in your field and access to the most recent scientific findings. Are you wondering what former students thought about your programme? Are you curious about what your education