Theorems · Theorem · commutative algebra
IsNilpotent.isUnit_quotient_mk_iff
∀ {R : Type u_2} [inst : CommRing R] {I : Ideal R},
IsNilpotent I → ∀ {x : R}, IsUnit ((Ideal.Quotient.mk I) x) ↔ IsUnit x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 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.
Cites30
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
- Nat.cast_oneproof · cited by 2,501
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- Ideal.mapproof · cited by 692
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_isLocalizationproof · cited by 6
- Ideal.Quotient.isUnit_mk_pow_iff_isUnit_mkproof · cited by 1
- StandardEtalePair.existsUnique_hasMap_of_hasMap_quotient_of_sq_eq_botproof · cited by 0