Theorems · Theorem · commutative algebra
Ideal.absNorm_span_singleton
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] [Module.Finite ℤ S]
(r : S), Ideal.absNorm (Ideal.span {r}) = ((Algebra.norm ℤ) r).natAbs- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapproof · cited by 10,215
- Idealstatement · cited by 4,748
- MonoidHomstatement and proof · cited by 3,629
- LinearMap.compproof · cited by 1,642
- map_zeroproof · cited by 1,614
- Module.Basisproof · cited by 1,477
- Module.Finitestatement and proof · cited by 1,032
- Ideal.spanstatement and proof · cited by 948
Cited by18
Results whose statement or proof uses this declaration.
- Ideal.natAbs_pow_inertiaDegproof · cited by 4
- Ideal.absNorm_eq_zero_iffproof · cited by 4
- Int.ideal_span_absNorm_eq_selfproof · cited by 4
- Ideal.norm_dvd_iffproof · cited by 3
- Ideal.finite_setOfPred_absNorm_eqproof · cited by 3
- IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_oneproof · cited by 2
- Ideal.absNorm_dvd_norm_of_memproof · cited by 1
- Ideal.absNorm_eq_pow_inertiaDegproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_ne_twoproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_two_powproof · cited by 1
- Ideal.absNorm_span_natCastproof · cited by 1
- IsPrimitiveRoot.card_quotient_toInteger_sub_oneproof · cited by 1