AlgebraExamTopics - (Topics for qualifying exam in algebra)...

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(Topics for qualifying exam in algebra) 731 SYLLABUS I. Set-up (over rings with unity, including noncommutative) Modules and Homomorphism Theorems Direct Sums and Products, Free Modules (including Universal Mapping Properties) Projective and Injective Modules, Divisible Modules Exact Sequences, Split Exact Sequences, Diagram Chasing Hom and Tensor (including left/right module structures induced on each, left/right exactness, behavior of projectives/injectives, flatness, and the adjoint isomorphism) II. Noncommutative Ring Theory Noetherian, Artinian, Hilbert Basis Theorem Composition Series, Length Semisimple Rings and Modules Maschke's Theorem Schur's Lemma Artin-Wedderburn Theorem Jacobson Radical, Nakayama's Lemma Artinian Rings Krull-Schmidt Theorem III. Additional Commutative Topic Localisation -------------------------------------------------------------------- -------------------------------------------------------------------- 731 SOURCES --------------------------------------------------------------------
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AlgebraExamTopics - (Topics for qualifying exam in algebra)...

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