Theorems · Theorem · commutative algebra
Ideal.ofList_cons_smul
∀ {R : Type u_7} [inst : CommSemiring R] (r : R) (rs : List R) {M : Type u_8} [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] (N : Submodule R M), Ideal.ofList (r :: rs) • N = r • N ⊔ Ideal.ofList rs • N- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Ideal.ofListstatement and proof · cited by 33
- Submodule.ideal_span_singleton_smulproof · cited by 7
- Submodule.sup_smulproof · cited by 4
- Ideal.ofList_consproof · cited by 3
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