Structures · Algebra
Ideal.IsPrime
An ideal P of a ring R is prime if P ≠ R and xy ∈ P → x ∈ P ∨ y ∈ P
- Defined in
- Mathlib.RingTheory.Ideal.Prime
- Shape
- One type argument · adds ne_top', mem_or_mem'
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by1
Concrete types that are instances5
- Polynomial
- NumberField.RingOfIntegers
- MvPolynomial
- Subtype
- HasQuotient.Quotient
How is a type an instance?
Loading the hierarchy index…
Assumed by616
- Ideal.primeCompl
- Localization.AtPrime
- Ideal.ResidueField
- IsLocalization.AtPrime
- Localization.localRingHom
- Ideal.Fiber
- Ideal.IsPrime.ne_top'
- HomogeneousLocalization.AtPrime
- Algebra.IsUnramifiedAt
- Localization.AtPrime.algebraOfLiesOver
- Algebra.QuasiFiniteAt
- Ideal.ResidueField.mapₐ
- IsLocalization.AtPrime.isLocalRing
- Algebra.WeaklyQuasiFiniteAt
- Ideal.primeCompl_le_nonZeroDivisors
- Localization.AtPrime.map_eq_maximalIdeal
- Ideal.exists_minimalPrimes_le
- Localization.localRingHom_to_map
- Ideal.inertiaDegIn_eq_inertiaDeg
- Localization.localRingHom_mk'
- Ideal.comap_isPrime
- IsLocalizedModule.AtPrime
- Ideal.map_isPrime_of_surjective
- Ideal.ramificationIdxIn_eq_ramificationIdx
- ValuationSubring.ofPrime
- Localization.le_comap_primeCompl_iff
- Ideal.disjoint_powers_iff_notMem_of_isPrime
- IsLocalization.AtPrime.to_map_mem_maximal_iff
- Localization.AtPrime.under_maximalIdeal
- Ideal.one_notMem
- Ideal.ResidueField.map
- IsLocalization.AtPrime.map_eq_maximalIdeal
- Ideal.inertiaDeg_pos
- PrimeSpectrum.primesOverOrderIsoFiber
- Ideal.ResidueField.algHom_ext
- IsLocalization.AtPrime.under_maximalIdeal
- Localization.localAlgHom
- Ideal.inertiaDeg_eq
- Ideal.exists_smul_eq_of_isGaloisGroup
- Ideal.ramificationIdx_def
- Ideal.IsDedekindDomain.ramificationIdx'_ne_zero_of_liesOver
- Ideal.ramificationIdx_eq
- Algebra.IsSmoothAt
- Ideal.IsPrime.mem_or_mem'
- IsLocalization.AtPrime.isPrime_map_of_liesOver
- Polynomial.residueFieldMapCAlgEquiv
- Ideal.ramificationIdx_pos
- Localization.localRingHom_comp
- Ideal.ker_algebraMap_residueField
- Ideal.isMaximal_of_isIntegral_of_isMaximal_comap
Ancestors0
No ancestors.