Theorems · Theorem · commutative algebra
isRadical_iff_span_singleton
∀ {R : Type u_1} {y : R} [inst : CommSemiring R], IsRadical y ↔ (Ideal.span {y}).IsRadical- Defined in
- Mathlib.RingTheory.Nilpotent.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsRadicalstatement and proof · cited by 30
- IsRadicalstatement · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Module.End.isSemisimple_of_squarefree_aeval_eq_zeroproof · cited by 4
- Module.End.IsSemisimple.minpoly_squarefreeproof · cited by 2
- isReduced_zmodproof · cited by 0