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 word field:
“Beat! beat! drums!—blow! bugles! blow!
Through the windows—through doors—burst like a ruthless force,
Into the solemn church, and scatter the congregation;
Into the school where the scholar is studying;
Leave not the bridegroom quiet—no happiness must he have now with his bride;
Nor the peaceful farmer any peace, plough his field or gathering his
grain;
So fierce you whirr and pound, you drums—so shrill you bugles blow.”
—Walt Whitman (1819–1892)