Theorems · Theorem · commutative algebra
Ideal.pointwise_smul_def
∀ {M : Type u_1} {R : Type u_3} [inst : Monoid M] [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] {a : M}
(S : Ideal R), a • S = Ideal.map (MulSemiringAction.toRingHom M R a) S- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 2 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.
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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Monoidstatement and proof · cited by 3,887
- Ideal.mapstatement · cited by 692
- MulSemiringActionstatement and proof · cited by 423
- Ideal.pointwiseDistribMulActionstatement · cited by 56
- MulSemiringAction.toRingHomstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_smulproof · cited by 2
- IsArithFrobAt.mem_stabilizerproof · cited by 1