理想类群 Ideal class group
（重定向自Ideal class）
理想类群是代数数论的基本对象之一，简称类群。它描述了一个数域的理想与元素的差异。理想类群是有限交换群，其元素个数称作该域的类数。
| 单词 | Ideal class |
| 释义 |
Ideal class
中文百科
理想类群 Ideal class group（重定向自Ideal class）
理想类群是代数数论的基本对象之一，简称类群。它描述了一个数域的理想与元素的差异。理想类群是有限交换群，其元素个数称作该域的类数。
英语百科
Ideal class group 理想类群（重定向自Ideal class）
In mathematics, for a field K an ideal class group (or class group) is the quotient group JK/PK where JK is the whole fractional ideals of K and PK is the principal ideals of K. The extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by the ideal class group (or class group). If this group is finite (as it is in the case of the ring of integers of a number field), then the order of the group is called the class number. The multiplicative theory of a Dedekind domain is intimately tied to the structure of its class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain. |
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