Theorems · Theorem · commutative algebra
CharP.quotient_iff_le_ker_natCast
∀ {R : Type u_1} [inst : CommRing R] (n : ℕ) [CharP R n] (I : Ideal R),
CharP (R ⧸ I) n ↔ Ideal.comap (Nat.castRingHom R) I ≤ RingHom.ker (Nat.castRingHom R)CharP.quotient_iff, but stated in terms of inclusions of ideals.
- Defined in
- Mathlib.Algebra.CharP.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- CharPstatement and proof · cited by 478
- Ideal.comapstatement and proof · cited by 443
- RingHom.kerstatement and proof · cited by 363
- Nat.castRingHomstatement and proof · cited by 27
- RingHom.ker_eq_comap_botproof · cited by 23
- CharP.quotient_iffproof · cited by 1
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