Theorems · Theorem · commutative algebra
RingHom.map_range
∀ {R : Type u} {S : Type v} {T : Type w} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] [inst_2 : NonAssocRing T]
(g : S →+* T) (f : R →+* S), Subring.map g f.range = (g.comp f).range- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Top.topproof · cited by 9,680
- RingHom.compstatement and proof · cited by 899
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- RingHom.rangestatement · cited by 138
- Subring.mapstatement and proof · cited by 33
- RingHom.range_eq_mapproof · cited by 1
- Subring.map_mapproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.canonicalEmbedding.mem_span_latticeBasisproof · cited by 0