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MAI0035
Algebra

Number of credits: 15 hp

Examiner: Leif Melkersson

Course Literature: Serge Lang: Algebra (Springer GTM#211).

Course contents: roups, operations, Sylow subgroups, structure of finitely generated abelian groups, categories and functors(universal constructions), free groups. Rings, rings of fractions, factorial domains , irreducibility criteria. Modules, free modules, modules over a principal ideal domain, exactness, lemme de serpent, limits, noetherian rings, Hilberts basis theorem, symmetric polynomials.
Algebraic field extensions, splitting fields, algebraic closure, separability, finite fields, transcendence bases. Multilinear maps, determinants, tensor products, symmetric and exterior algebras, Semisimplicity. Derivations. The Clifford algebra.

Organisation: Lectures, exercises (alt. reading course).

Examination: Solving assigned problems.

Prerequisites: Basic knowledge of algebra and linear algebra.


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Last updated: 2016-08-17