Theorems · Theorem · commutative algebra
Ideal.radical_bot_of_isReduced
∀ {R : Type u} [inst : CommSemiring R] [IsReduced R], ⊥.radical = ⊥- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsReduced
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- eq_bot_iffproof · cited by 159
- Ideal.radicalstatement · cited by 121
- IsReducedstatement and proof · cited by 98
- Ideal.isRadical_botproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.radical_bot_of_noZeroDivisorsproof · cited by 0