Theorems · Theorem · algebraic geometry
Module.rankAtStalk_eq_of_equiv
∀ {R : Type uR} {M : Type uM} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_1}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] (e : M ≃ₗ[R] N), Module.rankAtStalk M = Module.rankAtStalk N- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivstatement and proof · cited by 3,317
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
- Localization.AtPrimeproof · cited by 299
- LocalizedModule.mkLinearMapproof · cited by 76
- LinearEquiv.finrank_eqproof · cited by 65
- Module.rankAtStalkstatement · cited by 41
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.rankAtStalk_eq_of_isPushoutproof · cited by 3
- Module.rankAtStalk_isBaseChangeproof · cited by 2
- Module.Flat.tfae_algebraMap_surjectiveproof · cited by 1
- Module.rankAtStalk_tensorProduct_of_isScalarTowerproof · cited by 0
- Algebra.IsFiniteSplit.exists_tensorProduct_of_etaleproof · cited by 0