Theorems · Theorem · ring theory
Subalgebra.rangeS_algebraMap
∀ {R : Type u_3} {A : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
(S : Subalgebra R A), (algebraMap (↥S) A).rangeS = S.toSubsemiring- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomproof · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Subalgebrastatement and proof · cited by 1,353
- RingHom.compproof · cited by 899
- RingHomClass.toRingHomproof · cited by 746
- Subsemiringstatement and proof · cited by 456
- Subalgebra.toSubsemiringstatement and proof · cited by 115
- Subalgebra.valproof · cited by 104
- RingHom.rangeSstatement and proof · cited by 47
- Algebra.algebraMap_selfproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.setRange_algebraMapproof · cited by 3