Theorems · Theorem · commutative algebra
Subsemiring.map_comap_eq_self
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] {f : R →+* S} {t : Subsemiring S},
t ≤ f.rangeS → Subsemiring.map f (Subsemiring.comap f t) = t- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, 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.
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- inf_of_le_leftproof · cited by 186
- RingHom.rangeSstatement and proof · cited by 47
- Subsemiring.mapstatement and proof · cited by 29
- Subsemiring.comapstatement and proof · cited by 20
- Subsemiring.map_comap_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subsemiring.map_comap_eq_self_of_surjectiveproof · cited by 0