Examples
The following are integrally closed domains.
- Any principal ideal domain (in particular, any field).
- Any unique factorization domain (in particular, any polynomial ring over a unique factorization domain.)
- Any GCD domain (in particular, any Bézout domain or valuation domain).
- Any Dedekind domain.
- Any symmetric algebra over a field (since every symmetric algebra is isomorphic to a polynomial ring in several variables over a field).
Read more about this topic: Integrally Closed Domain
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“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)
“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)