Theorems · Theorem · commutative algebra
Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] [Module.Finite ℤ S]
{I : Ideal S}, Ideal.absNorm I ≠ 0 ↔ I ∈ nonZeroDivisors (Ideal S)- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Submonoidstatement · cited by 3,086
- Module.Finitestatement and proof · cited by 1,032
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Ideal.absNormstatement · cited by 123
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.absNorm_ne_zero_of_nonZeroDivisorsproof · cited by 3
- Ideal.card_norm_le_eq_card_norm_le_add_oneproof · cited by 2
- Ideal.absNorm_pos_iff_mem_nonZeroDivisorsproof · cited by 1