Theorems · Theorem · commutative algebra
Ideal.smul_mem_pointwise_smul
∀ {M : Type u_1} {R : Type u_3} [inst : Monoid M] [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] (m : M) (r : R)
(S : Ideal R), r ∈ S → m • r ∈ m • S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Monoidstatement and proof · cited by 3,887
- MulSemiringActionstatement and proof · cited by 423
- Ideal.subset_spanproof · cited by 86
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- Set.smul_mem_smul_setproof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.mem_pointwise_smul_iff_inv_smul_memproof · cited by 3
- Ideal.smul_mem_pointwise_smul_iffproof · cited by 0