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Categories and Functors, Products and Coproducts. Universal Objects. Fiber Products and Coproducts. Free Groups. Coproducts in The Category Of Groups and in The Category of Abelian Groups. Tensor Products. Linear Algebra Over Rings. Simple and Primitive Rings# Schur's Lemma, Jacobson Density Theorem, Wedderbruan-artin Theorem. Jacobson Radical, Semisimple Artinian Rings. Algebras Over Fields# Finite Dimensional Central Simple Algebras and Division Algebras. Tensor Products Of Algebras. Theorems of Frobenius, Skolem-noether, Wedderbrun. Double Centralizer Theorem. Splitting Fields. Crosssed Products And Cyclic Algebras. The Brauer Group of a Field.

Faculty: Mathematics
|Undergraduate Studies |Graduate Studies

Pre-required courses

(104158 - Introduction to Group Theory and 104279 - Introduction to Rings and Fields and 104280 - Modules)

• A first course in noncommutative rings - Lam, Tsit-Yuen
• A First Course in Noncommutative Rings [electronic resource] - Lam, T.Y.
• A First Course in Noncommutative Rings [electronic resource] - Lam, Tsit-Yuen.
• Associative algebras - Pierce, Richard S.
• Associative Algebras [electronic resource] - Pierce, R.S.
• Maximal orders - Reiner, Irving
• Maximal orders. - Reiner, Irving
• Noncommutative algebra - Farb, Benson
• Noncommutative Algebra [electronic resource] - Farb, Benson.
• Rational points on varieties - Poonen, Bjorn