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Theorems · Theorem · commutative algebra

Ideal.isPrimary_finsetInf

∀ {R : Type u_1} [inst : CommSemiring R] {ι : Type u_3} {s : Finset ι} {f : ι → Ideal R} {i : ι},
  i ∈ s →
    (∀ ⦃y : ι⦄, y ∈ s → (f y).IsPrimary) → (∀ ⦃y : ι⦄, y ∈ s → (f y).radical = (f i).radical) → (s.inf f).IsPrimary
Defined in
Mathlib.RingTheory.Ideal.IsPrimary
Cited by
1 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.isPrimary_finset_inf · cited by 0Ideal.isPrimary_finset_infFinset · cited by 13712FinsetCommSemiring · cited by 10911CommSemiringIdeal · cited by 4748IdealFinset.inf · cited by 219Finset.infIdeal.radical · cited by 121Ideal.radicalIdeal.IsPrimary · cited by 13Ideal.IsPrimarySubmodule.colon_univ · cited by 7Submodule.colon_univSubmodule.isPrimary_finsetInf · cited by 2Submodule.isPrimary_finse…Ideal.isPrimary_finsetInfCITED BYCITES

Cites8

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Cited by1

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