Theorems · Theorem · commutative algebra
Submodule.ideal_span_singleton_smul
∀ {R : Type u} {M : Type v} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (r : R)
(N : Submodule R M), Ideal.span {r} • N = r • N- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Submodule.span_eqproof · cited by 26
- Submodule.span_smul_spanproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Module.support_quotSMulTopproof · cited by 2
- Ideal.map_pointwise_smulproof · cited by 1
- FractionalIdeal.absNorm_div_norm_eq_absNorm_div_normproof · cited by 1
- Submodule.eq_bot_of_eq_pointwise_smul_of_mem_jacobson_annihilatorproof · cited by 1
- RingTheory.Sequence.eq_nil_of_isRegular_on_artinianproof · cited by 0
- Ideal.ofList_cons_smulproof · cited by 0
- Module.free_quotSMulTop_iff_freeproof · cited by 0