Theorems · Theorem · commutative algebra
IsLocalRing.exists_surjective_of_not_isLocalRing
∀ {R : Type u} [inst : CommRing R] [Nontrivial R], ¬IsLocalRing R → ∃ K₁ K₂ x x_1 f, Function.Surjective ⇑fThere exists a surjective ring homomorphism from a non-local commutative ring onto a product of two fields.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fieldstatement · cited by 7,404
- Idealproof · cited by 4,748
- Nontrivialstatement and proof · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- RingEquivproof · cited by 1,147
- RingHom.compproof · cited by 899
- Ideal.Quotient.mkproof · cited by 610
- Ideal.IsMaximalproof · cited by 452
- IsLocalRingstatement and proof · cited by 339
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.