Theorems · Theorem · commutative algebra
Ideal.map_sup
∀ {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 J : Ideal R) [RingHomClass F R S], Ideal.map f (I ⊔ J) = Ideal.map f I ⊔ Ideal.map f J- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomClassstatement and proof · cited by 193
- GaloisConnection.l_supproof · cited by 81
- Ideal.gc_map_comapproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- Ideal.ker_quotientMap_mkproof · cited by 1
- Ideal.smul_supproof · cited by 0