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)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“The ideal place for me is the one in which it is most natural to live as a foreigner.”
—Italo Calvino (1923–1985)
“The pursuit of Fashion is the attempt of the middle class to co-opt tragedy. In adopting the clothing, speech, and personal habits of those in straitened, dangerous, or pitiful circumstances, the middle class seeks to have what it feels to be the exigent and nonequivocal experiences had by those it emulates.”
—David Mamet (b. 1947)
“If we can learn ... to look at the ways in which various groups appropriate and use the mass-produced art of our culture ... we may well begin to understand that although the ideological power of contemporary cultural forms is enormous, indeed sometimes even frightening, that power is not yet all-pervasive, totally vigilant, or complete.”
—Janice A. Radway (b. 1949)