Examples of Ideal Class Groups
- The rings Z, Z, and Z, where ω is a cube root of 1 and i is a fourth root of 1 (i.e. a square root of −1), are all principal ideal domains, and so have class number 1: that is, they have trivial ideal class groups.
- If k is a field, then the polynomial ring k is an integral domain. It has a countably infinite set of ideal classes.
Read more about this topic: Ideal Class Group
Famous quotes containing the words examples of, examples, ideal, class and/or groups:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“Poetry, at all times, exercises two distinct functions: it may reveal, it may unveil to every eye, the ideal aspects of common things ... or it may actually add to the number of motives poetic and uncommon in themselves, by the imaginative creation of things that are ideal from their very birth.”
—Walter Pater (1839–1894)
“The history of all countries shows that the working class exclusively by its own effort is able to develop only trade-union consciousness.”
—Vladimir Ilyich Lenin (1870–1924)
“The awareness of the all-surpassing importance of social groups is now general property in America.”
—Johan Huizinga (1872–1945)