Theorems · Theorem · commutative algebra
Ring.ord_smul_of_isUnit
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_3} [inst_1 : CommRing S] [inst_2 : Algebra S R] {a : S},
IsUnit a → ∀ (x : R), Ring.ord R (a • x) = Ring.ord R xIn an S algebra R, the order of vanishing of x : R is equal to the order of vanishing
of a • x for a a unit in S.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- ENatstatement · cited by 4,985
- Algebra.algebraMapproof · cited by 4,706
- IsUnitstatement and proof · cited by 1,602
- Algebra.smul_defproof · cited by 287
- Ring.ordstatement and proof · cited by 28
- RingHom.isUnit_mapproof · cited by 14
- Ring.ord_mul_of_isUnit_leftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ring.ord_of_isUnitproof · cited by 2