Theorems · Theorem · commutative algebra
IsLocalRing.of_isMaximal_nilradical
∀ (R : Type u_1) [inst : CommSemiring R] [(nilradical R).IsMaximal], IsLocalRing R
- Defined in
- Mathlib.RingTheory.KrullDimension.Zero
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIdeal.IsMaximal
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Cites6
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
- Ideal.IsMaximalstatement and proof · cited by 452
- IsLocalRingstatement · cited by 339
- List.TFAE.outproof · cited by 177
- nilradicalstatement and proof · cited by 41
- Ring.krullDimLE_zero_and_isLocalRing_tfaeproof · cited by 7
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