Theorems · Theorem · commutative algebra
CharP.quotient_iff
∀ {R : Type u_1} [inst : CommRing R] (n : ℕ) [CharP R n] (I : Ideal R), CharP (R ⧸ I) n ↔ ∀ (x : ℕ), ↑x ∈ I → ↑x = 0CharP.quotient' as an Iff.
- Defined in
- Mathlib.Algebra.CharP.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- CharPstatement and proof · cited by 478
- CharP.cast_eq_zero_iffproof · cited by 42
- Submodule.Quotient.mk_eq_zeroproof · cited by 35
- CharP.quotient'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CharP.quotient_iff_le_ker_natCastproof · cited by 0