Examples
- The field of fractions of the ring of integers is the field of rationals, Q = Quot(Z).
- Let R := { a + b i | a,b in Z } be the ring of Gaussian integers. Then Quot(R) = {c + d i | c,d in Q}, the field of Gaussian rationals.
- The field of fractions of a field is isomorphic to the field itself.
- Given a field K, the field of fractions of the polynomial ring in one indeterminate K (which is an integral domain), is called the field of rational functions or field of rational fractions and is denoted K(X).
Read more about this topic: Field Of Fractions
Famous quotes containing the word examples:
“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)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“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)