Theorems · Theorem · commutative algebra
Ideal.comap_isPrime
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
(K : Ideal S) [inst_3 : RingHomClass F R S] [H : K.IsPrime], (Ideal.comap f K).IsPrimeVariant of Ideal.IsPrime.comap where ideal is explicit rather than implicit.
- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- FunLikestatement and proof · cited by 2,560
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.comapstatement · cited by 443
- RingHomClassstatement and proof · cited by 193
Cited by11
Results whose statement or proof uses this declaration.
- Ideal.isMaximal_comap_of_isIntegral_of_isMaximalproof · cited by 3
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomainproof · cited by 2
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isPrimeproof · cited by 2
- isJacobsonRing_of_isIntegralproof · cited by 1
- Ideal.map_radical_of_surjectiveproof · cited by 1
- IsLocalization.OverPrime.mem_normalizedFactors_of_isPrimeproof · cited by 1
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0
- Ideal.isPrime_map_C_iff_isPrimeproof · cited by 0
- Polynomial.isMaximal_comap_C_of_isMaximalproof · cited by 0
- Ring.DimensionLEOne.of_ringEquivproof · cited by 0