Theorems · Definition · commutative algebra
Ideal.pointwiseDistribMulAction
{M : Type u_1} →
{R : Type u_3} → [inst : Monoid M] → [inst_1 : Semiring R] → [MulSemiringAction M R] → DistribMulAction M (Ideal R)The action on an ideal corresponding to applying the action to every element.
This is available as an instance in the Pointwise locale.
- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 4,748
- Monoidstatement and proof · cited by 3,887
- DistribMulActionstatement · cited by 584
- MulSemiringActionstatement and proof · cited by 423
Cited by63
Results whose statement or proof uses this declaration.
- Ideal.Quotient.stabilizerHomstatement · cited by 10
- IsFractionRing.stabilizerHomstatement · cited by 8
- Ideal.exists_smul_eq_of_isGaloisGroupstatement · cited by 6
- Ideal.pointwise_smul_eq_comapstatement · cited by 5
- Algebra.IsInvariant.exists_smul_of_under_eqstatement · cited by 5
- Ideal.stabilizerEquivstatement · cited by 4
- Ideal.mem_pointwise_smul_iff_inv_smul_memstatement · cited by 3
- Ideal.pointwise_smul_defstatement · cited by 2
- Ideal.pointwise_smul_le_pointwise_smul_iffstatement · cited by 2
- Ideal.inertiaDeg_smulstatement · cited by 2
- Ideal.card_stabilizer_eqstatement · cited by 2
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankstatement · cited by 2