Theorems · Definition · commutative algebra
Subring.pointwiseMulAction
{M : Type u_1} →
{R : Type u_2} → [inst : Monoid M] → [inst_1 : Ring R] → [MulSemiringAction M R] → MulAction M (Subring R)The action on a subring corresponding to applying the action to every element.
This is available as an instance in the Pointwise locale.
- Defined in
- Mathlib.Algebra.Ring.Subring.Pointwise
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidRingMulSemiringAction
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.
- Ringstatement and proof · cited by 7,463
- Monoidstatement and proof · cited by 3,887
- MulActionstatement · cited by 1,294
- Subringstatement · cited by 602
- MulSemiringActionstatement and proof · cited by 423
Cited by23
Results whose statement or proof uses this declaration.
- Subring.pointwise_smul_defstatement · cited by 0
- Subring.pointwise_smul_le_iff₀statement · cited by 0
- Subring.pointwise_smul_le_pointwise_smul_iffstatement · cited by 0
- Subring.pointwise_smul_le_pointwise_smul_iff₀statement · cited by 0
- Subring.pointwise_smul_subset_iffstatement · cited by 0
- Subring.pointwise_smul_toAddSubgroupstatement · cited by 0
- Subring.pointwise_smul_toSubsemiringstatement · cited by 0
- Subring.mem_inv_pointwise_smul_iffstatement · cited by 0
- Subring.mem_inv_pointwise_smul_iff₀statement · cited by 0
- Subring.mem_pointwise_smul_iff_inv_smul_memstatement · cited by 0
- Subring.mem_pointwise_smul_iff_inv_smul_mem₀statement · cited by 0
- Subring.mem_smul_pointwise_iff_existsstatement · cited by 0