Theorems · Theorem · commutative algebra
Ideal.subset_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 T : Ideal R}, S ≤ a • T ↔ a⁻¹ • S ≤ T- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- MulSemiringActionstatement and proof · cited by 423
- inv_smul_smulproof · cited by 76
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- Ideal.pointwise_smul_le_pointwise_smul_iffproof · cited by 2
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