Math 806 Notes on Galois Theory
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چکیده
3 Extensions of rings and fields 14 3.1 Symmetric polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Integral ring extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Prime ideals in Z[x]: elementary classification . . . . . . . . . . . . . . . . . . . . . . 19 3.4 The spectrum of a commutative ring . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4.1 Spec(Z[x]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.5 Algebraic field extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.5.1 The ring of algebraic integers and the field of algebraic numbers . . . . . . . . 24 3.6 Field extensions of finite degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 ∗Thanks to Beth Romano for careful reading and corrections
منابع مشابه
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تاریخ انتشار 2012