Overring
Encyclopedia
In mathematics, an overring B of an integral domain A is a subring of the field of fractions
K of A that contains A: i.e.,
.
A typical example is given by localization: if S is a multiplicatively closed subset of A, then the localization S−1A is an overring of A. In fact, every overring of Z arises in this way.
Field of fractions
In abstract algebra, the field of fractions or field of quotients of an integral domain is the smallest field in which it can be embedded. The elements of the field of fractions of the integral domain R have the form a/b with a and b in R and b ≠ 0...
K of A that contains A: i.e.,
.A typical example is given by localization: if S is a multiplicatively closed subset of A, then the localization S−1A is an overring of A. In fact, every overring of Z arises in this way.