Basic Results
- An affine algebraic set V is a variety if and only if I(V) is a prime ideal; equivalently, V is a variety if and only if its coordinate ring is an integral domain.
- Every nonempty affine algebraic set may be written uniquely as a union of algebraic varieties (where none of the sets in the decomposition are subsets of each other).
- Let k be the coordinate ring of the variety V. Then the dimension of V is the transcendence degree of the field of fractions of k over k.
Read more about this topic: Algebraic Variety
Famous quotes containing the words basic and/or results:
“The basic Female body comes with the following accessories: garter belt, panti-girdle, crinoline, camisole, bustle, brassiere, stomacher, chemise, virgin zone, spike heels, nose ring, veil, kid gloves, fishnet stockings, fichu, bandeau, Merry Widow, weepers, chokers, barrettes, bangles, beads, lorgnette, feather boa, basic black, compact, Lycra stretch one-piece with modesty panel, designer peignoir, flannel nightie, lace teddy, bed, head.”
—Margaret Atwood (b. 1939)
“We do not raise our children alone.... Our children are also raised by every peer, institution, and family with which they come in contact. Yet parents today expect to be blamed for whatever results occur with their children, and they expect to do their parenting alone.”
—Richard Louv (20th century)