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)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“The whole point about the true unconscious is that it is all the time moving forward, beyond the range of its own fixed laws or habits. It is no good trying to superimpose an ideal nature upon the unconscious.”
—D.H. (David Herbert)
“Think of what our Nation stands for,
Books from Boots’ and country lanes,
Free speech, free passes, class distinction,
Democracy and proper drains.”
—Sir John Betjeman (1906–1984)
“screenwriter
Policemen so cherish their status as keepers of the peace and protectors of the public that they have occasionally been known to beat to death those citizens or groups who question that status.”
—David Mamet (b. 1947)