Theorems · Definition · commutative algebra
ValuationSubring.pointwiseHasSMul
{K : Type u} →
[inst : Field K] → {G : Type u_1} → [inst_1 : Group G] → [MulSemiringAction G K] → SMul G (ValuationSubring K)The action on a valuation subring corresponding to applying the action to every element.
This is available as an instance in the Pointwise locale.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldGroupMulSemiringAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- Subringproof · cited by 602
- MulSemiringActionstatement and proof · cited by 423
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.toSubringproof · cited by 32
Cited by10
Results whose statement or proof uses this declaration.
- ValuationSubring.mem_smul_pointwise_iff_existsstatement · cited by 0
- ValuationSubring.smul_mem_pointwise_smulstatement · cited by 0
- ValuationSubring.smul_mem_pointwise_smul_iffstatement · cited by 0
- ValuationSubring.subset_pointwise_smul_iffstatement · cited by 0
- ValuationSubring.coe_pointwise_smulstatement · cited by 0
- ValuationSubring.mem_inv_pointwise_smul_iffstatement · cited by 0
- ValuationSubring.mem_pointwise_smul_iff_inv_smul_memstatement · cited by 0
- ValuationSubring.pointwise_smul_le_pointwise_smul_iffstatement · cited by 0
- ValuationSubring.pointwise_smul_subset_iffstatement · cited by 0
- ValuationSubring.pointwise_smul_toSubringstatement · cited by 0