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Introduction - Algebra 1
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Algebra 1
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- 1 Introduction - Algebra 1
- 2 Permutations
- 3 Group Axioms
- 4 Order and Conjugacy
- 5 Subgroups
- 6 Problem solving
- 7 Group Actions
- 8 Cosets
- 9 Group Homomorphisms
- 10 Normal subgroups
- 11 Qutient Groups
- 12 Product and Chinese Remainder Theorem
- 13 Dihedral Groups
- 14 Semidirect products
- 15 Problem solving
- 16 The Orbit Counting Theorem
- 17 Fixed points of group actions
- 18 Second application: Fixed points of group actions
- 19 Sylow Theorems - a preliminary proposition
- 20 Sylow Theorem I
- 21 Problem solving I
- 22 Problem solving II
- 23 Sylow Theorem II
- 24 Sylow Theorem III
- 25 Problem solving I
- 26 Problem solving II
- 27 Free Groups I
- 28 Free Groups IIa
- 29 Free Groups IIb
- 30 Free Groups III
- 31 Free Groups IV
- 32 Problem Solving/Examples
- 33 Generators and relations for symmetric groups – I
- 34 Generators and relations for symmetric groups – II
- 35 Definition of a Ring
- 36 Euclidean Domains
- 37 Gaussian Integers
- 38 The Fundamental Theorem of Arithmetic
- 39 Divisibility and Ideals
- 40 Factorization and the Noetherian Condition
- 41 Examples of Ideals in Commutative Rings
- 42 Problem Solving/Examples
- 43 The Ring of Formal Power Series
- 44 Fraction Fields
- 45 Path Algebra of a Quiver
- 46 Ideals In Non Commutative Rings
- 47 Product of Rings
- 48 Ring Homomorphisms
- 49 Quotient Rings
- 50 Problem solving
- 51 Tensor and Exterior Algebras
- 52 Modules : definition
- 53 Modules over polynomial rings $K[x]$
- 54 Modules: alternative definition
- 55 Modules: more examples
- 56 Submodules
- 57 General constructions of submodules
- 58 Problem solving
- 59 Quotient modules
- 60 Homomorphisms
- 61 More examples of homomorphisms
- 62 First isomorphism theorem
- 63 Direct sums of modules
- 64 Complementary submodules
- 65 Change of ring
- 66 Problem solving
- 67 Free Modules (finitely generated)
- 68 Determinants
- 69 Primary Decomposition
- 70 Problem solving
- 71 Finitely generated modules and the Noetherian condition
- 72 Counterexamples to the Noetherian condition
- 73 Generators and relations for Finitely Generated Modules
- 74 General Linear Group over a Commutative Ring
- 75 Equivalence of Matrices
- 76 Smith Canonical Form for a Euclidean domain
- 77 solved_problems1
- 78 Smith Canonical Form for PID
- 79 Structure of finitely generated modules over a PID
- 80 Structure of a finitely generated abelian group
- 81 Similarity of Matrices
- 82 Deciding Similarity
- 83 Rational Canonical Form
- 84 Jordan Canonical Form
