jacobson — Mathlib

English

For a submodule N ≤ jacobson R M, the Jacobson radical of the quotient M/N corresponds to the image of jacobson under the quotient map.

Русский

Если N ≤ jacobson(R M), то радикал Якобсона квоты M/N равен образу jacobson под квотно-мэппингом.

LaTeX

$$N \le \mathrm{jacobson}(R M) \Rightarrow \mathrm{jacobson}(R, M / N) = map N.mkQ (\mathrm{jacobson}(R M))$$

Lean4

/-- The Jacobson radical of `I` is the infimum of all maximal (left) ideals containing `I`. -/
def jacobson (I : TwoSidedIdeal R) : TwoSidedIdeal R :=
  (asIdeal I).jacobson.toTwoSided

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