Theorems · Theorem · commutative algebra
Ideal.le_comap_map
∀ {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}
{I : Ideal R} [inst_3 : RingHomClass F R S], I ≤ Ideal.comap f (Ideal.map f I)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.mapstatement · cited by 692
- Ideal.comapstatement · cited by 443
- RingHomClassstatement and proof · cited by 193
- GaloisConnection.le_u_lproof · cited by 52
- Ideal.gc_map_comapproof · cited by 17
Cited by18
Results whose statement or proof uses this declaration.
- Ideal.giMapComapproof · cited by 6
- Ideal.map_eq_top_or_isMaximal_of_surjectiveproof · cited by 6
- Ideal.comap_map_eq_self_of_faithfullyFlatproof · cited by 4
- Ideal.comap_map_of_bijectiveproof · cited by 3
- Ideal.comap_map_eq_self_of_isMaximalproof · cited by 2
- IsLocalization.under_map_of_isPrimary_disjointproof · cited by 2
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimesproof · cited by 1
- Ideal.map_under_le_under_mapproof · cited by 1
- Ideal.ker_quotientMap_mkstatement and proof · cited by 1
- Ideal.quotient_mk_maps_eqstatement · cited by 1
- Ideal.injective_quotient_le_comap_mapstatement · cited by 1