Theorems · Theorem · commutative algebra
Subring.map_comap_eq_self_of_surjective
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S},
Function.Surjective ⇑f → ∀ (t : Subring S), Subring.map f (Subring.comap f t) = t- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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Cites8
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
- Subring.mapstatement · cited by 33
- Subring.comapstatement · cited by 22
- RingHom.range_eq_top_of_surjectiveproof · cited by 1
- Subring.map_comap_eq_selfproof · cited by 1
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