Localization interface for derivation-Ore extensions #
The proposition below is the exact output expected from a theorem saying that localizing a derivation-Ore extension at coefficients gives the derivation-Ore extension of the localized coefficient ring. It packages data and its compatibility law; it does not assert that the data exist.
def
AlgebraicAnalysis.OreLocalizationExtension.IsDerivationOreLocalization
{B : Type u_1}
[Ring B]
(D : OreDivisionDerivation B)
(S : Submonoid B)
[OreLocalization.OreSet S]
[OreLocalization.OreSet (Submonoid.map (↑(OreAssociativity.normalCoefficient D)) S)]
:
Existence of data identifying the localization of NormalOre D along coefficient
denominators with a derivation-Ore extension of the localized coefficient
ring. Ore-ness of both denominator sets remains an explicit hypothesis.
Equations
- One or more equations did not get rendered due to their size.