Theorems · Theorem · ring theory
Subalgebra.center_prod
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B],
Subalgebra.center R (A × B) = (Subalgebra.center R A).prod (Subalgebra.center R B)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement · cited by 1,353
- SetLike.coe_injectiveproof · cited by 374
- Subalgebra.centerstatement and proof · cited by 24
- Subalgebra.prodstatement and proof · cited by 11
- Set.center_prodproof · cited by 10
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