Theorems · Theorem · commutative algebra
Module.Flat.of_linearEquiv
∀ {R : Type u} {M : Type v} {N : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] [Module.Flat R M] (e : N ≃ₗ[R] M), Module.Flat R NAn R-module linearly equivalent to a flat R-module is flat.
- Defined in
- Mathlib.RingTheory.Flat.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- LinearMap.idproof · cited by 625
- Module.Flatstatement and proof · cited by 279
- LinearEquiv.self_trans_symmproof · cited by 15
- Module.Flat.of_retractproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- RingHom.Flat.of_bijectiveproof · cited by 8
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatproof · cited by 2
- Module.Flat.equiv_iffproof · cited by 2
- Module.Flat.of_uliftproof · cited by 1
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1
- RingHom.Flat.lTensorproof · cited by 1
- Module.Flat.isBaseChangeproof · cited by 1
- Module.FaithfullyFlat.of_linearEquivproof · cited by 1
- Ideal.Pure.of_isIdempotentElemproof · cited by 0
- Module.Flat.of_shrinkproof · cited by 0