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Completely reducible, artinian, and noetherian rings and modules. Free, projective, and injective modules. The Krull-Remak-Schmidt Theorem. Introduction to the representation theory of finite dimensional algebras.
Last update: T_KA (19.05.2010)
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F.W.Anderson, K.R.Fuller: Rings and Categories of Modules, 2nd ed.,Springer, New York, 1992. D. S. Passman, A Course in Ring Theory, AMS, Providence, 2004. I. Assem, D. Simson, A. Skowronski, Elements of the Representation Theory of Associative Algebras. Vol. 1, Cambridge Univ. Press, Cambridge, 2006. Last update: T_KA (19.05.2010)
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Contents of the Lecture: Ring theory (Jacobson radical, structure of completely reducible modules and rings, Wedderburn-Artin Theorem. Artinian and noetherian rings and modules, Hopkins Theorem, Hilbert Basis Theorem.) Module theory (Free and projective modules, Kaplansky theorems. Injective modules, The Baer Criterion, injetive hulls, structure of injective modules over noetherian rings, structure of divisible abelian groups, hereditary rings). Supplementary topic: Envelopes and covers of modules. Projective and flat covers. Example class: Examples. The Krull-Remak-Schmidt Theorem. Elements of the representation theory of finite dimensional algebras (path algebras of quivers, their Jacobson radical and heredity, linear representations of quivers as modules over path algebras). Last update: T_KA (19.05.2010)
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Knowledge of basics of algebra at the level of Algebra I (NALG026). Last update: T_KA (19.05.2010)
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