Theorems · Theorem · commutative algebra
Ideal.mem_inv_pointwise_smul_iff
∀ {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⁻¹ • S ↔ a • x ∈ S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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
- Groupstatement and proof · cited by 6,238
- Idealstatement and proof · cited by 4,748
- inv_invproof · cited by 494
- MulSemiringActionstatement and proof · cited by 423
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- Ideal.mem_pointwise_smul_iff_inv_smul_memproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsInvariant.exists_smul_of_under_eqproof · cited by 5