Theorems · Definition · commutative algebra
seminormFromConst
{R : Type u_1} → [inst : CommRing R] → {c : R} → {f : RingSeminorm R} → f 1 ≤ 1 → f c ≠ 0 → IsPowMul ⇑f → RingSeminorm RThe function seminormFromConst is a RingSeminorm on R.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- RingSeminormstatement and proof · cited by 58
- IsPowMulstatement and proof · cited by 39
- seminormFromConst'proof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- normFromConstproof · cited by 1
- algNormFromConst_defstatement · cited by 0
- seminormFromConst_defstatement · cited by 0