منابع مشابه
Normal Bases of Ray Class Fields over Imaginary Quadratic Fields
We first develop a criterion to determine normal bases (Theorem 2.4), and by making use of necessary lemmas which were refined from [3] we further prove that singular values of certain Siegel functions form normal bases of ray class fields over all imaginary quadratic fields other than Q( √−1) and Q( √−3) (Theorem 4.5 and Remark 4.6). This result would be an answer for the Lang-Schertz conjectu...
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Let F be an algebraic number field and E a quadratic extension with E = F(√μ). We describe a minimal set of elements for generating the integral elements oE of E as an oF module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of E as well. In the last section, we present examples of...
متن کاملClass field theory : ray class groups and ray class fields
In the previous lecture we proved the Kronecker-Weber theorem: every abelian extension L of Q lies in a cyclotomic extension Q(ζm)/Q. The isomorphism Gal(Q(ζm)/Q) ' (Z/mZ)× allows us to view Gal(L/Q) as a quotient of (Z/mZ)×. Conversely, for each quotient H of (Z/mZ)×, there is a subfield L of Q(ζm) for which H ' Gal(L/Q). We now want make the correspondence between H and L explicit, and then g...
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Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L over Q(√ −3) is given. This RIB simplifies and completes the one given by Haghighi (1986).
متن کاملOn Gröbner bases and Krull dimension of residue class rings of polynomial rings over integral domains
Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...
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ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2006
ISSN: 1015-8634
DOI: 10.4134/bkms.2006.43.1.077