Theorems · Theorem · commutative algebra
Ideal.zero_mem
∀ {α : Type u} [inst : Semiring α] (I : Ideal α), 0 ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Submodule.zero_memproof · cited by 58
Cited by37
Results whose statement or proof uses this declaration.
- Ideal.primeCompl_le_nonZeroDivisorsproof · cited by 17
- Ideal.eq_bot_of_comap_eq_botproof · cited by 9
- Ideal.ker_le_comapproof · cited by 8
- Ideal.mem_image_of_mem_map_of_surjectiveproof · cited by 6
- DividedPowers.dpow_eval_zeroproof · cited by 4
- Ideal.subset_union_primeproof · cited by 4
- PadicInt.zmod_cast_comp_toZModPowproof · cited by 4
- DividedPowers.span_isSubDPIdeal_iffproof · cited by 3
- PrimeSpectrum.exists_comap_evalRingHom_eqproof · cited by 3
- MaximalSpectrum.iInf_localization_eq_botproof · cited by 3
- Submodule.mem_ideal_smul_span_iff_exists_sumproof · cited by 3
- Ideal.IsPrime.mem_or_mem_of_mul_eq_zeroproof · cited by 3