= Totally positive element of a number field
{title2=$\sigma_v(a)>0\text{ at every real place}$}
= Totally positive
{synonym}
A nonzero element of a <number field> is totally positive when its image is positive under every real <field embedding>. In a totally real <number field>, the <principal fractional ideals> having a <totally positive> generator form the subgroup used to define the <narrow ideal class group>. Signs of different generators are related by the <unit signature map>.
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