Theorems · Definition · commutative algebra

RingEquiv.ofLeftInverseS

{R : Type u} →
  {S : Type v} →
    [inst : NonAssocSemiring R] →
      [inst_1 : NonAssocSemiring S] → {g : S → R} → {f : R →+* S} → Function.LeftInverse g ⇑f → R ≃+* ↥f.rangeS

Restrict a ring homomorphism with a left inverse to a ring isomorphism to its RingHom.rangeS.

Defined in: Mathlib.Algebra.Ring.Subsemiring.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NonAssocSemiring NonAssocSemiring

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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
RingEquivstatement · cited by 1,147
NonAssocSemiringstatement and proof · cited by 805
Subsemiringstatement · cited by 456
RingHom.rangeSstatement and proof · cited by 47
Subsemiring.subtypeproof · cited by 11
RingHom.rangeSRestrictproof · cited by 4

Cited by2

Results whose statement or proof uses this declaration.

RingEquiv.ofLeftInverseS_applystatement · cited by 0
RingEquiv.ofLeftInverseS_symm_applystatement · cited by 0