Theorems · Theorem · commutative algebra
RingHom.finite_localizationPreserves
RingHom.LocalizationPreserves @RingHom.Finite
If S is a finite R-algebra, then S' = M⁻¹S is a finite R' = M⁻¹R-algebra.
- Defined in
- Mathlib.RingTheory.RingHom.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingproof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomproof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- Submonoidproof · cited by 3,086
- Module.Finiteproof · cited by 1,032
- RingHom.compproof · cited by 899
- IsLocalizationproof · cited by 636
- RingHom.toAlgebraproof · cited by 337
- Submonoid.mapproof · cited by 190
- Algebra.algebraMapSubmonoidproof · cited by 137
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.localization_away_map_finiteproof · cited by 0