Theorems · Theorem · commutative algebra

RingCon.rangeS_lift

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

Given a congruence relation c on a semiring 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

2 results in Mathlib

Foundations

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

Assumes

NonAssocSemiringNonAssocSemiring