Theorems · Theorem · commutative algebra
Prime.isMaximal_span_singleton
∀ {R : Type u_1} [inst : CommSemiring R] [NoZeroDivisors R] [Ring.KrullDimLE 1 R] {a : R},
Prime a → (Ideal.span {a}).IsMaximal- Defined in
- Mathlib.RingTheory.KrullDimension.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 948
- NoZeroDivisorsstatement and proof · cited by 545
- Ideal.IsMaximalstatement · cited by 452
- Primestatement and proof · cited by 277
- Ring.KrullDimLEstatement and proof · cited by 79
- Prime.ne_zeroproof · cited by 47
- Ideal.span_singleton_primeproof · cited by 27
- Ideal.IsPrime.isMaximal_of_ne_botproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.liesOver_span_iffproof · cited by 1