Theorems · Theorem · ring theory
Subalgebra.pointwise_smul_toSubmodule
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {R' : Type u_3}
[inst_3 : Semiring R'] [inst_4 : MulSemiringAction R' A] [inst_5 : SMulCommClass R' R A] (m : R')
(S : Subalgebra R A), Subalgebra.toSubmodule (m • S) = m • Subalgebra.toSubmodule S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Submodulestatement · cited by 7,192
- SMulCommClassstatement and proof · cited by 1,927
- Subalgebrastatement and proof · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- MulSemiringActionstatement and proof · cited by 423
- Subalgebra.toSubmodulestatement · cited by 141
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Subalgebra.pointwiseMulActionstatement · cited by 5
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