Module MA3412: Integral Domains, Modules and Algebraic Integers
نویسندگان
چکیده
2 Integral Domains 12 2.1 Factorization in Integral Domains . . . . . . . . . . . . . . . . 12 2.2 Euclidean Domains . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Principal Ideal Domains . . . . . . . . . . . . . . . . . . . . . 16 2.4 Fermat’s Two Squares Theorem . . . . . . . . . . . . . . . . . 17 2.5 Maximal Ideals and Prime Ideals . . . . . . . . . . . . . . . . 20 2.6 Unique Factorization Domains . . . . . . . . . . . . . . . . . . 23 2.7 Prime Ideals of Principal Ideal Domains . . . . . . . . . . . . 25 2.8 An Integral Domain lacking Unique Factorization . . . . . . . 26 2.9 Rings of Polynomials with Coefficients in a Unique Factorization Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.10 Polynomial Rings in Several Indeterminates . . . . . . . . . . 36 2.11 Rings of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.12 Integrally Closed Domains . . . . . . . . . . . . . . . . . . . . 46 2.13 Irreducibility of Polynomials over Fields of Fractions . . . . . 47 2.14 Requirements for Unique Factorization Of Ideals . . . . . . . . 47
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