overring
Let be a commutative ring having regular elements and let be the total ring of fractions
of . Then . Every subring of containing is an overring of .
Example. Let be a rational prime number. The -integral rational numbers (http://planetmath.org/PAdicValuation) are the quotients of two integers such that the divisor (http://planetmath.org/Division) is not divisible by . The set of all -integral rationals is an overring of .