map_jacobson_le — Mathlib

English

Under a surjective ring hom f, the image of jacobson R contains jacobson R₂, i.e. map_jacobson_le: Submodule.map f(jacobson R) ≤ jacobson R₂.

Русский

При сюръекции f: R → R₂ образ jacobson R содержит jacobson R₂: Submodule.map f(jacobson R) ≤ jacobson R₂.

LaTeX

$$$\\operatorname{Submodule.map}_{f}(\\operatorname{jacobson}(R)) \\le \\operatorname{jacobson}(R_2).$$$

Lean4

theorem map_jacobson_le : Submodule.map f.toSemilinearMap (jacobson R) ≤ jacobson R₂ :=
  Module.map_jacobson_le f.toSemilinearMap

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