Theorems · Theorem · ring theory
Algebra.IsCentral.left_of_tensor
∀ (K : Type u_1) (B : Type u_2) (C : Type u_3) [inst : CommSemiring K] [inst_1 : Semiring B] [inst_2 : Semiring C]
[inst_3 : Algebra K B] [inst_4 : Algebra K C],
Function.Injective ⇑(algebraMap K C) →
∀ [Module.Flat K B] [hbc : Algebra.IsCentral K (TensorProduct K B C)], Algebra.IsCentral K B- Defined in
- Mathlib.Algebra.Central.TensorProduct
- Cited by
- 2 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.
Cites20
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Bot.botproof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- LE.le.transproof · cited by 3,151
- TensorProductstatement and proof · cited by 2,545
- RingHomClass.toRingHomproof · cited by 746
- AlgHom.toRingHomproof · cited by 490
- Module.Flatstatement and proof · cited by 279
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsCentral.right_of_tensorproof · cited by 1
- Algebra.IsCentral.left_of_tensor_of_fieldproof · cited by 0