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Theorems · Definition · number theory

IsPrimitiveRoot.toInteger

{K : Type u} → [inst : Field K] → {ζ : K} → {k : ℕ} → [NeZero k] → IsPrimitiveRoot ζ k → NumberField.RingOfIntegers K

Abbreviation to see a primitive root of unity as a member of the ring of integers.

Defined in
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic
Cited by
72 results in Mathlib
Foundations
Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNeZero

Around this declaration

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

IsPrimitiveRoot.toInteger_isPrimitiveRoot · cited by 15IsPrimitiveRoot.toInteger…IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two · cited by 5IsPrimitiveRoot.norm_toIn…IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one · cited by 4Rat.inertiaDeg_span_zeta_…IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one · cited by 4Rat.ramificationIdx_span_…IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver · cited by 3Rat.eq_span_zeta_sub_one_…IsPrimitiveRoot.integralPowerBasisOfPrimePow_gen · cited by 3IsPrimitiveRoot.integralP…IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two · cited by 3IsPrimitiveRoot.norm_toIn…IsCyclotomicExtension.Rat.adjoin_singleton_eq_top · cited by 3Rat.adjoin_singleton_eq_t…IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one · cited by 3Rat.associated_norm_zeta_…IsCyclotomicExtension.Rat.discr_prime_pow · cited by 2Rat.discr_prime_powIsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver' · cited by 2Rat.eq_span_zeta_sub_one_…IsPrimitiveRoot.zeta_sub_one_prime · cited by 2IsPrimitiveRoot.zeta_sub_…IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton · cited by 2Rat.isIntegralClosure_adj…IsCyclotomicExtension.Rat.ncard_primesOver_of_prime_pow · cited by 2Rat.ncard_primesOver_of_p…IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one · cited by 2Three.lambda_dvd_or_dvd_s…Field · cited by 7404FieldNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersIsPrimitiveRoot · cited by 356IsPrimitiveRootIsPrimitiveRoot.toIntegerCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by72

Results whose statement or proof uses this declaration.