ray class group

Let ${\\mathfrak{m}}$ be a modulus for a number field $K$ . The ray class group of $K$ mod ${\\mathfrak{m}}$ is the group $\\mathbb{I}^{\\mathfrak{m}}/K_{{\\mathfrak{m}},1}$ , where

•
$\\mathbb{I}^{\\mathfrak{m}}$ is the subgroup of the ideal group of $K$ generated by all prime ideals which do not occur in the factorization of ${\\mathfrak{m}}$ .
•
$K_{{\\mathfrak{m}},1}$ is the subgroup of $\\mathbb{I}^{\\mathfrak{m}}$ consisting of all principal ideals in the ring of integers of $K$ having the form $(\\alpha)$ where $\\alpha$ is multiplicatively congruent to $1\\bmod{\\mathfrak{m}}$ .

单词	RayClassGroup
释义	ray class group Let ${\\mathfrak{m}}$ be a modulus for a number field $K$ . The ray class group of $K$ mod ${\\mathfrak{m}}$ is the group $\\mathbb{I}^{\\mathfrak{m}}/K_{{\\mathfrak{m}},1}$ , where • $\\mathbb{I}^{\\mathfrak{m}}$ is the subgroup of the ideal group of $K$ generated by all prime ideals which do not occur in the factorization of ${\\mathfrak{m}}$ . • $K_{{\\mathfrak{m}},1}$ is the subgroup of $\\mathbb{I}^{\\mathfrak{m}}$ consisting of all principal ideals in the ring of integers of $K$ having the form $(\\alpha)$ where $\\alpha$ is multiplicatively congruent to $1\\bmod{\\mathfrak{m}}$ .
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