= Narrow ideal class group
{title2=$\operatorname{Cl}^{+}(K)$}
= Narrow class group
{synonym}
The narrow ideal class group of a <number field> is the group of nonzero <fractional ideals> modulo <principal fractional ideals> generated by <totally positive> elements. It is the <ray class group> for the modulus consisting of all real <Archimedean places> and trivial finite part. The forgetful map to the ordinary <ideal class group> is surjective, with <kernel> $\{\pm1\}^{r_1}/\operatorname{sgn}(\mathcal O_K^\times)$ under the <unit signature map>.
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