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:
“blind wantons like the gulls who scream
And rip the edge off any ideal or dream.”
—Louis MacNeice (1907–1963)
“There might be a class of beings, human once, but now to humanity invisible, for whose scrutiny, and for whose refined appreciation of the beautiful, more especially than for our own, had been set in order by God the great landscape-garden of the whole earth.”
—Edgar Allan Poe (1809–1849)
“The virtue of dress rehearsals is that they are a free show for a select group of artists and friends of the author, and where for one unique evening the audience is almost expurgated of idiots.”
—Alfred Jarry (1873–1907)