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Theorems · Theorem · commutative algebra

Ideal.absNorm_bot

∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S], Ideal.absNorm ⊥ = 0
Defined in
Mathlib.RingTheory.Ideal.Norm.AbsNorm
Cited by
4 results in Mathlib
Foundations
Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDedekindDomainModule.Free
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.absNorm_span_singleton · cited by 18Ideal.absNorm_span_single…Ideal.absNorm_eq_zero_iff · cited by 4Ideal.absNorm_eq_zero_iffIdeal.absNorm_pow_inertiaDeg · cited by 2Ideal.absNorm_pow_inertia…Ideal.absNorm_relNorm · cited by 2Ideal.absNorm_relNormDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingIdeal · cited by 4748IdealBot.bot · cited by 4720Bot.botmap_zero · cited by 1614map_zeroMonoidWithZeroHom · cited by 704MonoidWithZeroHomIsDedekindDomain · cited by 668IsDedekindDomainModule.Free · cited by 597Module.FreeIdeal.absNorm · cited by 123Ideal.absNormIdeal.zero_eq_bot · cited by 27Ideal.zero_eq_botIdeal.absNorm_botCITED BYCITES

Cites10

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Cited by4

Results whose statement or proof uses this declaration.