Theorems · Theorem · commutative algebra

RingCon.lift_injective_iff

∀ {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}, Function.Injective ⇑(c.lift f h) ↔ c = RingCon.ker f

Given a ring homomorphism f from M to P whose kernel contains c, the lift of M to P is injective iff ker f = c.

Defined in

Mathlib.RingTheory.Congruence.Hom

Cited by

1 results in Mathlib

Foundations

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

Assumes

NonAssocSemiringNonAssocSemiring