Theorems · Theorem · ring theory
Subalgebra.pointwise_smul_toSubring
∀ {R' : Type u_4} {R : Type u_5} {A : Type u_6} [inst : Semiring R'] [inst_1 : CommRing R] [inst_2 : Ring A]
[inst_3 : MulSemiringAction R' A] [inst_4 : Algebra R A] [inst_5 : SMulCommClass R' R A] (m : R')
(S : Subalgebra R A), (m • S).toSubring = m • S.toSubring- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- SMulCommClassstatement and proof · cited by 1,927
- Subalgebrastatement and proof · cited by 1,353
- Subringstatement · cited by 602
- MulSemiringActionstatement and proof · cited by 423
- Subalgebra.toSubringstatement · cited by 30
- Subring.pointwiseMulActionstatement · cited by 23
- Subalgebra.pointwiseMulActionstatement · cited by 5
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