Theorems · Theorem · commutative algebra
Ideal.Quotient.isUnit_mk_pow_iff_isUnit_mk
∀ {S : Type u_1} [inst : CommRing S] (I : Ideal S) {x : S} {n : ℕ},
n ≠ 0 → (IsUnit ((Ideal.Quotient.mk (I ^ n)) x) ↔ IsUnit ((Ideal.Quotient.mk I) x))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
Cites14
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- HasQuotient.Quotientstatement · cited by 2,301
- IsUnitstatement and proof · cited by 1,602
- Ideal.mapproof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
- isUnit_map_iffproof · cited by 17
- Ideal.pow_le_selfproof · cited by 16
- Ideal.map_quotient_selfproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Quotient.isUnit_mk_pow_iff_notMemproof · cited by 1