Theorems · Theorem · commutative algebra
AdicCompletion.ofTensorProductInvOfPiFintype_comp_ofTensorProduct
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (ι : Type u_4) [inst_1 : Fintype ι] [inst_2 : DecidableEq ι],
↑(AdicCompletion.ofTensorProductInvOfPiFintype I ι) ∘ₗ AdicCompletion.ofTensorProduct I (ι → R) = LinearMap.id- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Idealstatement and proof · cited by 4,748
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compstatement and proof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- LinearMap.idstatement and proof · cited by 625
- AdicCompletionstatement and proof · cited by 160
- LinearMap.comp_assocproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.ofTensorProductEquivOfPiFintypeproof · cited by 1