Theorems · Theorem · commutative algebra
ClassGroup.integralRep_mem_nonZeroDivisors
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] {I : FractionalIdeal (nonZeroDivisors R) (FractionRing R)},
I ≠ 0 → I.num ∈ nonZeroDivisors (Ideal R)- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Idealstatement · cited by 4,748
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- FractionalIdealstatement and proof · cited by 423
- FractionRingstatement and proof · cited by 200
- mem_nonZeroDivisors_iff_ne_zeroproof · cited by 38
- FractionalIdeal.numstatement and proof · cited by 22
- FractionalIdeal.num_eq_zero_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ClassGroup.mk0_surjectiveproof · cited by 5
- ClassGroup.mk0_integralRepstatement and proof · cited by 1