Theorems · Theorem · commutative algebra
Subring.map_comap_eq_self
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S} {t : Subring S},
t ≤ f.range → Subring.map f (Subring.comap f t) = t- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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.
- RingHomstatement and proof · cited by 10,189
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- inf_of_le_leftproof · cited by 186
- RingHom.rangestatement and proof · cited by 138
- Subring.mapstatement and proof · cited by 33
- Subring.comapstatement and proof · cited by 22
- Subring.map_comap_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subring.map_comap_eq_self_of_surjectiveproof · cited by 0