If R is a given integral domain, the smallest field containing R as a subring is uniquely determined up to isomorphism and is called the field of fractions or quotient field of R. It can be thought of as consisting of all fractions a/b with a and b in R and b ≠ 0, modulo an appropriate equivalence relation. The field of fractions of the integers is the field of rational numbers. The field of fractions of a field is isomorphic to the field itself.
Read more about this topic: Integral Domain
Famous quotes containing the words field of and/or field:
“A field of water betrays the spirit that is in the air. It is continually receiving new life and motion from above. It is intermediate in its nature between land and sky.”
—Henry David Thoreau (1817–1862)
“In the field of world policy I would dedicate this Nation to the policy of the Good Neighbor—the neighbor who resolutely respects himself and, because he does, respects the rights of others—the neighbor who respects his obligations and respects the sanctity of his agreements in and with a world of neighbors.”
—Franklin D. Roosevelt (1882–1945)