Theorems · Definition · commutative algebra
Ideal.prod
{R : Type u} → {S : Type v} → [inst : Semiring R] → [inst_1 : Semiring S] → Ideal R → Ideal S → Ideal (R × S)I × J as an ideal of R × S.
- Defined in
- Mathlib.RingTheory.Ideal.Prod
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Ideal.comapproof · cited by 443
- RingHom.sndproof · cited by 39
- RingHom.fstproof · cited by 36
Cited by30
Results whose statement or proof uses this declaration.
- Ideal.ideal_prod_eqstatement · cited by 4
- Ideal.isPrime_ideal_prod_topstatement · cited by 2
- Ideal.isPrime_of_isPrime_prod_topstatement and proof · cited by 2
- Ideal.map_prodComm_prodstatement and proof · cited by 2
- Ideal.prod_bot_botstatement and proof · cited by 2
- Ideal.prod_injstatement · cited by 2
- Ideal.prod_top_topstatement · cited by 2
- Ideal.idealProdEquivproof · cited by 2
- Ideal.ideal_prod_primestatement and proof · cited by 2
- Ideal.mem_prodstatement · cited by 2
- Ideal.isPrime_ideal_prod_top'statement and proof · cited by 1
- Ideal.map_fst_prodstatement and proof · cited by 1