Theorems · Theorem · commutative algebra
Ideal.mem_pointwise_smul_iff_inv_smul_mem
∀ {M : Type u_1} {R : Type u_3} [inst : Group M] [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] {a : M}
{S : Ideal R} {x : R}, x ∈ a • S ↔ a⁻¹ • x ∈ S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 3 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.
Cites8
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
- Groupstatement and proof · cited by 6,238
- Idealstatement and proof · cited by 4,748
- MulSemiringActionstatement and proof · cited by 423
- inv_smul_smulproof · cited by 76
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- smul_inv_smulproof · cited by 53
- Ideal.smul_mem_pointwise_smulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.mem_inv_pointwise_smul_iffproof · cited by 1
- Ideal.inertia_le_stabilizerproof · cited by 1
- Ideal.under_smulproof · cited by 1