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)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“There is no dream of love, however ideal it may be, which does not end up with a fat, greedy baby hanging from the breast.”
—Charles Baudelaire (1821–1867)
“He could jazz up the map-reading class by having a full-size color photograph of Betty Grable in a bathing suit, with a co- ordinate grid system laid over it. The instructor could point to different parts of her and say, “Give me the co-ordinates.”... The Major could see every unit in the Army using his idea.... Hot dog!”
—Norman Mailer (b. 1923)
“Some of the greatest and most lasting effects of genuine oratory have gone forth from secluded lecture desks into the hearts of quiet groups of students.”
—Woodrow Wilson (1856–1924)