Theorems · Theorem · commutative algebra
Ideal.pointwise_smul_eq_comap
∀ {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), a • S = Ideal.comap (RingEquiv.symm ((MulSemiringAction.toRingAut M R) a)) S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 5 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Groupstatement and proof · cited by 6,238
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- RingEquivstatement · cited by 1,147
- Ideal.mapproof · cited by 692
- RingEquiv.symmstatement and proof · cited by 567
- Ideal.comapstatement · cited by 443
- MulSemiringActionstatement and proof · cited by 423
- Ideal.extproof · cited by 131
- Ideal.pointwiseDistribMulActionstatement · cited by 56
Cited by5
Results whose statement or proof uses this declaration.
- IsArithFrobAt.conjproof · cited by 1
- Ideal.smul_underproof · cited by 0
- Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_auxproof · cited by 0
- Ideal.Quotient.stabilizerHom_surjective_of_profiniteproof · cited by 0
- Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0