Theorems · Theorem · commutative algebra
isPrincipalIdealRing_prod_iff
∀ {R : Type u} {S : Type u_1} [inst : Semiring R] [inst_1 : Semiring S],
IsPrincipalIdealRing (R × S) ↔ IsPrincipalIdealRing R ∧ IsPrincipalIdealRing S- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- IsPrincipalIdealRingstatement and proof · cited by 131
- RingHom.sndproof · cited by 39
- RingHom.fstproof · cited by 36
- Prod.snd_surjectiveproof · cited by 22
- Prod.fst_surjectiveproof · cited by 22
- IsPrincipalIdealRing.of_surjectiveproof · cited by 4
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