Ideal Class Group
In mathematics, 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 a certain group known as an 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.
Read more about Ideal Class Group: History and Origin of The Ideal Class Group, Definition, Properties, Relation With The Group of Units, Examples of Ideal Class Groups, Connections To Class Field Theory
Famous quotes containing the words ideal, class and/or group:
“The ideal of the self-sufficient American family is a myth, dangerous because most families, especially affluent families, do in fact make use of a range of services to survive. Families needing one or another kind of help are not morally deficient; most families do need assistance at one time or another.”
—Joseph Featherstone (20th century)
“God of justice, save the people
From the clash of race and creed,
From the strife of class and faction,
Make our nation free indeed;”
—William Pierson Merrill (1867–1954)
“No other group in America has so had their identity socialized out of existence as have black women.... When black people are talked about the focus tends to be on black men; and when women are talked about the focus tends to be on white women.”
—bell hooks (b. c. 1955)