Theorems · Theorem · ring theory
Algebra.IsCentral.left_of_tensor_of_field
∀ (K : Type u_4) (B : Type u_5) (C : Type u_6) [inst : Field K] [inst_1 : Ring B] [inst_2 : Ring C] [Nontrivial C] [inst_4 : Algebra K B] [inst_5 : Algebra K C] [Algebra.IsCentral K (TensorProduct K B C)], Algebra.IsCentral K B
Let B and C be two algebras over a field K, if B ⊗[K] C is central and C is
non-trivial, then B is central.
- Defined in
- Mathlib.Algebra.Central.TensorProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- TensorProductstatement and proof · cited by 2,545
- Nontrivialstatement and proof · cited by 2,416
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- Algebra.IsCentralstatement and proof · cited by 17
- Algebra.IsCentral.left_of_tensorproof · cited by 2
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