quotientKerEquivRangeS — Mathlib

English

Redundant reinforcement: As soon as R is a semiring, HahnSeries Γ R forms a semiring.

Русский

Повтор: если R семиринг, то HahnSeries Γ R образует семиринг.

LaTeX

$$$[Semiring R] \\Rightarrow Semiring(\\mathrm{HahnSeries}(\\Gamma,R))$$$

Lean4

/-- The **first isomorphism theorem** for commutative rings (`RingHom.rangeS` version). -/
noncomputable def quotientKerEquivRangeS (f : R →+* S) : R ⧸ ker f ≃+* f.rangeS :=
  (Ideal.quotEquivOfEq f.ker_rangeSRestrict.symm).trans <| quotientKerEquivOfSurjective f.rangeSRestrict_surjective

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