Theorems · Theorem · commutative algebra
Subring.comap_map_eq_self_of_injective
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S},
Function.Injective ⇑f → ∀ (s : Subring R), Subring.comap f (Subring.map f s) = s- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- SetLike.coe_injectiveproof · cited by 374
- Subsemigroup.carrierproof · cited by 160
- Submonoid.toSubsemigroupproof · cited by 159
- Subsemiring.toSubmonoidproof · cited by 153
- Set.preimage_image_eqproof · cited by 87
- Subring.toSubsemiringproof · cited by 71
- Subring.mapstatement and proof · cited by 33
- Subring.comapstatement and proof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- CommRingCat.closure_range_union_range_eq_top_of_isPushoutproof · cited by 1