Corps biquadratiques monogènes

Corps biquadratiques monogènes
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单基因双二次军团

DOI：
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发表时间：
1995
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影响因子：
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通讯作者：
François Tanoé
François Tanoé
中科院分区：
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文献类型：
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作者：
M. Gras;François Tanoé

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AbstractLet
AbstractLet $$K = mathbb{Q}(sqrt {dm} ,sqrt {dn} )$$ be a biquadratic number field (where d,m,n∈ℤ, are uniquely determined); we say that it is monogenic if its ring of integers OK is of the form ℤ[θ]. We show that K is monogenic if and only if the two following conditions are satisfied:(i)2δm=2δn+4(2−δd) where δ=0 or 1 is defined by mn≡(−1)δ mod4;(ii)the equation (u2-v2)2(2δm)-(u2+v2)2(2δn)=±1 has solutions in ℤ. We characterize all the imaginary monogenic biquadratic fieds and establishe other necessary conditions for monogenicity of real fields. Conjectures, numerical tables and statistics are given.