Prime Discriminant Factorization of Discriminants of Algebraic Number Fields
Prime Discriminant Factorization of Discriminants of Algebraic Number Fields
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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.
What to read after Prime Discriminant Factorization of Discriminants of Algebraic Number Fields?
You can find similar books in the "Read Also" column, or choose other free books by Davis, Danny Nevin to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Prime Discriminant Factorization of Discriminants of Algebraic Number Fields?
You can find similar books in the "Read Also" column, or choose other free books by Davis, Danny Nevin to read onlineMoreLess
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