Theorems · Theorem · commutative algebra
Submodule.coe_span_smul
∀ {R' : Type u_1} {M' : Type u_2} [inst : CommSemiring R'] [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
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Finsuppproof · cited by 5,255
- Idealstatement · cited by 4,748
- mul_commproof · cited by 2,262
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.span_smul_eqproof · cited by 6