| Introduction Remarks on Notation and Terminology Chapter 1 Basics 1.1 The Definitions 1.2 Fields and Vector Spaces 1.3 Matrices 1.4 Modules 1.5 The Language of Categories Chapter 2 Linear Algebras and Artinian Rings, 2.1 Linear Algebras 2.2 Chain Conditions 2.3 Artinian Rings: the Semisimple Case 2.4 Artinian Rings: the Radical 2.5 The Krull-Schmidt Theorem 2.6 Group Representations. Definitions and General Properties 2.7 Group Characters Chapter 3 Noetherian Rings 3.1 Polynomial Rings 3.2 The Euclidean Algorithm 3.3 Factorization 3.4 Principal Ideal Domains 3.5 Modules over Principal Ideal Domains 3.6 Algebraic Integers Chapter 4 PAng Constructions 4.1 The Direct Product of Rings 4.2 The Axiom of Choice and Zorn's Lemma 4.3 Tensor Products of Modules and Algebras 4.4 Modules over General Rings 4.5 Projective Modules 4.6 Injective Modules 4.7 Invariant Basis Number and Projective-Free Rings Chapter 5 General Rings 5.1 Rings of Fractions 5.2 Skew Polynomial Rings 5.3 Free Algebras and Tensor Rings 5.4 Free Ideal Rings Outline Solutions Notations and Symbols Bibliography Index |
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