Course 311: Michaelmas Term 2005 Part III: Topics in Commutative Algebra
نویسنده
چکیده
3 Topics in Commutative Algebra 2 3.1 Rings and Fields . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Quotient Rings and Homomorphisms . . . . . . . . . . . . . . 5 3.4 The Characteristic of a Ring . . . . . . . . . . . . . . . . . . . 7 3.5 Polynomial Rings in Several Variables . . . . . . . . . . . . . . 7 3.6 Algebraic Sets and the Zariski Topology . . . . . . . . . . . . 10 3.7 Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.8 Noetherian Modules . . . . . . . . . . . . . . . . . . . . . . . 15 3.9 Noetherian Rings and Hilbert’s Basis Theorem . . . . . . . . . 18 3.10 The Structure of Algebraic Sets . . . . . . . . . . . . . . . . . 21 3.11 Maximal Ideals and Zorn’s Lemma . . . . . . . . . . . . . . . 23 3.12 Prime Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.13 Affine Varieties and Irreducibility . . . . . . . . . . . . . . . . 26 3.14 Radical Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
منابع مشابه
Course MA2C03, Michaelmas Term 2014 Section 2: Abstract Algebra
2 Abstract Algebra 24 2.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 24 2.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 24 2.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 24 2.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 The General Associative Law . . . . . . . . . . . . . . . . . . 26 2.6 Identity el...
متن کاملCourse 311: Michaelmas Term 2005 Part I: Topics in Number Theory
1 Topics in Number Theory 2 1.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 2 1.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 2 1.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 3 1.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 5 1.6 The Infini...
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3 Abstract Algebra 33 3.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 33 3.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 33 3.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 33 3.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 The General Associative Law . . . . . . . . . . . . . . . . . . 35 3.6 Identity el...
متن کاملCourse 311: Michaelmas Term 2005 Part II: Topics in Group Theory
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