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单词 Overring
释义

overring


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 .

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