Theorems · Theorem · commutative algebra
Ideal.isPrime_ideal_prod_top
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {I : Ideal R} [h : I.IsPrime], (I.prod ⊤).IsPrime- Defined in
- Mathlib.RingTheory.Ideal.Prod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.prodstatement · cited by 28
- Ideal.IsPrime.mem_or_memproof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.ideal_prod_primeproof · cited by 2
- Ideal.isPrime_ideal_prod_top'proof · cited by 1