Prime Discriminant Factorization of Discriminants of Algebraic Number Fields

Davis, Danny Nevin

The book Prime Discriminant Factorization of Discriminants of Algebraic Number Fields was written by author Davis, Danny Nevin Here you can read free online of Prime Discriminant Factorization of Discriminants of Algebraic Number Fields book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Prime Discriminant Factorization of Discriminants of Algebraic Number Fields a good or bad book?

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Let d , be a cyclic ^-discriminant . First note that 2 \ d , since 2^1 mod I and l± 2. Therefore d . = 1 mod 4. So, l-l in particular, the prime absolute cyclic ^-discriminants are p for 19 2(t-l) p = 1 mod Z and Z . But d , differs from a product of such prime discriminants by at most a sign. Since every discriminant involved is congruent to 1 mod 4 the result follows.
SECTION V THE CASE OF QUADRATIC DISCRIMINANT IDEALS In this section we will characterize the algebraic number fields that have... the property of prime discriminant factorization of quadratic discriminant ideals. In the next section we will show that this same characterization holds in the case of quadratic idele discriminants.
We shall prove some preliminary results, the first of which is " well known " but for which a detailed proof was not found by the author in the literature.
Proposition 8. Let L = K(/a) b r . a quadratic extension of K with a a square free integer of K. Suppose that p is a prime K-ideal.
We assume (without loss of generality) that either v n (°0 = or 1.

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