The Maximal Unramified Extensions of the Imaginary Quadratic Number Fields with Class Number Two
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چکیده
منابع مشابه
Unramified Quaternion Extensions of Quadratic Number Fields
The first mathematician who studied quaternion extensions (H8-extensions for short) was Dedekind [6]; he gave Q( √ (2 + √ 2)(3 + √ 6) ) as an example. The question whether given quadratic or biquadratic number fields can be embedded in a quaternion extension was extensively studied by Rosenblüth [32], Reichardt [31], Witt [36], and Damey and Martinet [5]; see Ledet [19] and the surveys [15] and...
متن کاملThe Dirichlet Class Number Formula for Imaginary Quadratic Fields
because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. Algebra lets us define a group that measures the failure, geometry shows that the group is finite, and analysis yields the formula for its order. To move forward through the main storyline without b...
متن کاملThe Dirichlet Class Number Formula for Imaginary Quadratic Fields
Z[ √ −5] = {a+ b √ −5 : a, b ∈ Z}, because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. Algebra lets us define a group that measures the failure, geometry shows that the group is finite, and analysis yields the formula for its order. To move forward t...
متن کاملThe Dirichlet Class Number Formula for Imaginary Quadratic Fields
Z[ √ −5] = {a+ b √ −5 : a, b ∈ Z}, because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. The large-scale methodology deserves immediate note, before the reader is immersed in a long succession of smaller attention-filling specifics: • algebra lets us d...
متن کاملThe Dirichlet Class Number Formula for Imaginary Quadratic Fields
Z[ √ −5] = {a+ b √ −5 : a, b ∈ Z}, because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. The large-scale methodology deserves immediate note, before the reader is immersed in a long succession of smaller attention-filling specifics: • algebra lets us d...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1996
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0111