Theorems · Theorem · commutative algebra
Submodule.span_smul_eq
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (s : Set R)
(N : Submodule R M), Ideal.span s • N = s • N- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- Ideal.spanstatement · cited by 948
- Submodule.pointwiseSetSMulstatement · cited by 30
- Submodule.coe_set_smulproof · cited by 2
- Submodule.coe_span_smulproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- Ideal.smul_restrictScalarsproof · cited by 3
- Submodule.restrictScalars_map_smul_eqproof · cited by 2
- Submodule.top_ne_set_smul_of_subset_jacobson_annihilatorproof · cited by 1
- Submodule.set_smul_top_eq_spanproof · cited by 0
- Submodule.eq_bot_of_set_smul_eq_of_subset_jacobson_annihilatorproof · cited by 0