Theorems · Theorem · commutative algebra

RingCon.range_lift

∀ {M : Type u_1} {P : Type u_3} [inst : Ring M] [inst_1 : Ring P] {c : RingCon M} {f : M →+* P} (H : c ≤ RingCon.ker f),
  (c.lift f H).range = f.range

Given a congruence relation c on a ring and a homomorphism f constant on the equivalence classes of c, f has the same image as the homomorphism that f induces on the quotient.

Defined in

Mathlib.RingTheory.Congruence.Hom

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRing