Theorems · Theorem · commutative algebra
RingHom.Flat.comp_iff_of_bijective_left
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
{f : R →+* S} {g : S →+* T}, Function.Bijective ⇑g → ((g.comp f).Flat ↔ f.Flat)- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- RingHomstatement and proof · cited by 10,189
- RingEquivproof · cited by 1,147
- RingHom.compstatement and proof · cited by 899
- Function.Bijectivestatement and proof · cited by 863
- RingEquiv.symmproof · cited by 567
- RingHom.extproof · cited by 331
- RingEquiv.toRingHomproof · cited by 150
- RingHom.Flatstatement and proof · cited by 60
- RingEquiv.symm_apply_applyproof · cited by 30
- RingEquiv.ofBijectiveproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.Flat.ulift_iffproof · cited by 1