overringOverring2004-05-21 17:53:062008-05-10 13:42:26Definitiontotal ring of fractions% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $R$ be a commutative ring having regular elements and let $T$ be the total ring of fractions of $R$. \,Then \,$R \subseteq T$. \,Every subring of $T$ containing $R$ is an {\em overring} of $R$.\\
\textbf{Example.}\, Let $p$ be a rational prime number.\, The \PMlinkname{$p$-integral rational numbers}{PAdicValuation} are the quotients of two integers such that the \PMlinkname{divisor}{Division} is not divisible by $p$.\, The set of all $p$-integral rationals is an overring of $\mathbb{Z}$.