Theorems · Theorem · commutative algebra
RingHom.map_rangeS
∀ {R : Type u} {S : Type v} {T : Type w} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S]
[inst_2 : NonAssocSemiring T] (g : S →+* T) (f : R →+* S), Subsemiring.map g f.rangeS = (g.comp f).rangeS- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingHom.rangeSstatement · cited by 47
- Subsemiring.mapstatement and proof · cited by 29
- Subsemiring.map_mapproof · cited by 1
- RingHom.rangeS_eq_mapproof · cited by 1
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