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)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“I simply contend that the middle-class ideal which demands that people be affectionate, respectable, honest and content, that they avoid excitements and cultivate serenity is the ideal that appeals to me, it is in short the ideal of affectionate family life, of honorable business methods.”
—Gertrude Stein (1874–1946)
“I know no East or West, North or South, when it comes to my class fighting the battle for justice. If it is my fortune to live to see the industrial chain broken from every workingman’s child in America, and if then there is one black child in Africa in bondage, there shall I go.”
—Mother Jones (1830–1930)
“Writers and politicians are natural rivals. Both groups try to make the world in their own images; they fight for the same territory.”
—Salman Rushdie (b. 1947)