Theorems · Theorem · linear algebra
IsLocalization.finrank_eq
∀ {R : Type uR} (S : Type uS) {N : Type uN} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : AddCommGroup N]
[inst_3 : Module R N] [inst_4 : Algebra R S] [inst_5 : Module S N] [IsScalarTower R S N] (p : Submonoid R)
[IsLocalization p S], p ≤ nonZeroDivisors R → Module.finrank S N = Module.finrank R N- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- Module.finrankstatement · cited by 1,770
- nonZeroDivisorsstatement and proof · cited by 895
- IsLocalizationstatement and proof · cited by 636
- Module.rankproof · cited by 496
- Cardinal.toNatproof · cited by 153
Cited by1
Results whose statement or proof uses this declaration.
- IsFractionRing.finrank_right_eqproof · cited by 1