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:
“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)
“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)
“As to the family, I have never understood how that fits in with the other ideals—or, indeed, why it should be an ideal at all. A group of closely related persons living under one roof; it is a convenience, often a necessity, sometimes a pleasure, sometimes the reverse; but who first exalted it as admirable, an almost religious ideal?”
—Rose Macaulay (1881–1958)
“The great disadvantage, and advantage, of the small urban bourgeois is his limited outlook. He sees the world as a middle- class world, and everything outside these limits is either laughable or slightly wicked.”
—George Orwell (1903–1950)
“In properly organized groups no faith is required; what is required is simply a little trust and even that only for a little while, for the sooner a man begins to verify all he hears the better it is for him.”
—George Gurdjieff (c. 1877–1949)