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Theorems · Theorem · commutative algebra

Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot

∀ {R : Type u} [inst : CommRing R] {I : Ideal R}, I.jacobson = I ↔ ⊥.jacobson = ⊥

An ideal I of R is equal to its Jacobson radical if and only if the Jacobson radical of the quotient ring R/I is the zero ideal

Defined in
Mathlib.RingTheory.Jacobson.Ideal
Cited by
2 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing

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