Ideal.isPrimary_iff

∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R},
  I.IsPrimary ↔ I ≠ ⊤ ∧ ∀ {x y : R}, x * y ∈ I → x ∈ I ∨ y ∈ I.radical

A proper ideal I is primary iff xy ∈ I implies x ∈ I or y ∈ radical I.

Defined in: Mathlib.RingTheory.Ideal.IsPrimary
Cited by: 4 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring

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