Theorems · Theorem · commutative algebra
RingHom.Flat.of_bijective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S}, Function.Bijective ⇑f → f.FlatBijective ring maps are flat.
- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 110 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.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- LinearEquiv.symmproof · cited by 1,461
- Function.Bijectivestatement and proof · cited by 863
- RingHom.toAlgebraproof · cited by 337
- Algebra.linearMapproof · cited by 157
- RingHom.Flatstatement · cited by 60
- LinearEquiv.ofBijectiveproof · cited by 60
- Module.Flat.of_linearEquivproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrankproof · cited by 6
- RingHom.Flat.comp_iff_of_bijective_rightproof · cited by 2
- RingHom.Flat.comp_iff_of_bijective_leftproof · cited by 1
- RingHom.finrank_comp_right_of_bijectiveproof · cited by 1
- RingHom.Flat.respectsIsoproof · cited by 1
- RingHom.Flat.ulift_iffproof · cited by 1
- RingHom.FaithfullyFlat.of_bijectiveproof · cited by 1
- RingHom.Flat.tensorProductMapproof · cited by 0