FractionCategory

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FractionCategory

$\begin{usage} FractionCategory~R: Category \end{usage}$

$\begin{params} {\em R} & \htmlref{\texttt{IntegralDomain}}{IntegralDomain} & an integral domain\\ \end{params}$

$\begin{descr} FractionCategory~R is the category of subrings of the fraction field of R. \end{descr}$

Exports

Algebra R

DifferentialExtension R

IntegralDomain

LinearAlgebraRing

denominator: % $\to$ R Denominator of a fraction

normalize: % $\to$ % Normalize a fraction

numerator: % $\to$ R Numerator of a fraction

if R has CharacteristicZero then
CharacteristicZero

if R has FactorizationRing then
FactorizationRing

if R has FiniteCharacteristic then
FiniteCharacteristic

if R has RationalRootRing then
RationalRootRing

if R has Specializable then
Specializable

if R has UnivariateGcdRing then
UnivariateGcdRing

Subsections

Next: denominator,numerator Up: Commutative Algebra Previous: shift Contents Index

Manuel Bronstein 2000-12-13

`Algebra` R
`DifferentialExtension` R
`IntegralDomain`
`LinearAlgebraRing`
`denominator`:	% $\to$ R	Denominator of a fraction
`normalize`:	% $\to$ %	Normalize a fraction
`numerator`:	% $\to$ R	Numerator of a fraction