Let R be a commutative ring having regular elementsPlanetmathPlanetmath and let T be the total ring of fractionsMathworldPlanetmath of R.  Then  RT.  Every subring of T containing R is an overring of R.

Example.  Let p be a rational prime number.  The p-integral rational numbers (http://planetmath.org/PAdicValuation) are the quotients of two integers such that the divisorMathworldPlanetmathPlanetmath (http://planetmath.org/Division) is not divisible by p.  The set of all p-integral rationals is an overring of .

Title overring
Canonical name Overring
Date of creation 2013-03-22 14:22:33
Last modified on 2013-03-22 14:22:33
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 12
Author pahio (2872)
Entry type Definition
Classification msc 13B30
Related topic AConditionOfAlgebraicExtension