Theorems · Theorem · commutative algebra
Ideal.comap_comap
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {T : Type u_3} [inst_2 : Semiring T] {I : Ideal T}
(f : R →+* S) (g : S →+* T), Ideal.comap f (Ideal.comap g I) = Ideal.comap (g.comp f) I- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- RingHom.compstatement · cited by 899
- Ideal.comapstatement · cited by 443
Cited by27
Results whose statement or proof uses this declaration.
- Ideal.map_mapproof · cited by 37
- RingHom.comap_kerproof · cited by 16
- Algebra.FinitePresentation.equivproof · cited by 9
- Algebra.FinitePresentation.ker_fG_of_surjectiveproof · cited by 7
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- Ideal.ramificationIdx'_comap_eqproof · cited by 2
- Ideal.inertiaDeg'_comap_eqproof · 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
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Ideal.map_under_le_under_mapproof · cited by 1
- Ideal.comp_quotientMap_eq_of_comp_eqstatement · cited by 1