Theorems · Theorem · ring theory
Ring.map_jacobson_le
∀ {R : Type u_1} {R₂ : Type u_2} [inst : Ring R] [inst_1 : Ring R₂] (f : R →+* R₂) [inst_2 : RingHomSurjective f],
Submodule.map f.toSemilinearMap (Ring.jacobson R) ≤ Ring.jacobson R₂- Defined in
- Mathlib.RingTheory.Jacobson.Radical
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingRingRingHomSurjective
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Submodule.mapstatement · cited by 614
- RingHomSurjectivestatement and proof · cited by 220
- Ring.jacobsonstatement · cited by 37
- RingHom.toSemilinearMapstatement and proof · cited by 18
- Module.map_jacobson_leproof · cited by 2
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