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Theorems · Theorem · number theory

Polynomial.cyclotomic.irreducible_rat

∀ {n : ℕ}, 0 < n → Irreducible (Polynomial.cyclotomic n ℚ)

cyclotomic n ℚ is irreducible.

Defined in
Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
Cited by
18 results in Mathlib
Foundations
Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

IsCyclotomicExtension.Rat.finrank · cited by 4Rat.finrankIsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_two · cited by 4Rat.nrComplexPlaces_eq_to…IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two · cited by 3IsPrimitiveRoot.norm_toIn…IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow · cited by 3Rat.isIntegralClosure_adj…IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow · cited by 2IsPrimitiveRoot.norm_toIn…IsCyclotomicExtension.Rat.discr_prime_pow · cited by 2Rat.discr_prime_powIsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two · cited by 1IsPrimitiveRoot.norm_toIn…IsPrimitiveRoot.norm_toInteger_sub_one_eq_one · cited by 1IsPrimitiveRoot.norm_toIn…IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow' · cited by 1Rat.discr_prime_pow_eq_un…IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two · cited by 1IsPrimitiveRoot.zeta_sub_…IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow · cited by 1IsPrimitiveRoot.zeta_sub_…Polynomial.cyclotomic.isCoprime_rat · cited by 1cyclotomic.isCoprime_ratIsPrimitiveRoot.dvd_of_isCyclotomicExtension · cited by 1IsPrimitiveRoot.dvd_of_is…IsCyclotomicExtension.Rat.three_pid · cited by 0Rat.three_pidIsCyclotomicExtension.Rat.discr_odd_prime' · cited by 0Rat.discr_odd_prime'Polynomial · cited by 5681PolynomialIrreducible · cited by 496IrreduciblePolynomial.cyclotomic · cited by 130Polynomial.cyclotomicPolynomial.map_cyclotomic_int · cited by 21Polynomial.map_cyclotomic…Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map · cited by 4IsPrimitive.irreducible_i…Polynomial.cyclotomic.isPrimitive · cited by 2cyclotomic.isPrimitivePolynomial.cyclotomic.irreducible · cited by 1cyclotomic.irreduciblecyclotomic.irreducible_ratCITED BYCITES

Cites7

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

Cited by18

Results whose statement or proof uses this declaration.