Theorems · Definition · commutative algebra

Subring.equivMapOfInjective

{R : Type u} →
  {S : Type v} →
    [inst : NonAssocRing R] →
      [inst_1 : NonAssocRing S] → (s : Subring R) → (f : R →+* S) → Function.Injective ⇑f → ↥s ≃+* ↥(Subring.map f s)

A subring is isomorphic to its image under an injective function

Defined in

Mathlib.Algebra.Ring.Subring.Basic

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocRingNonAssocRing