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Theorems · Definition · ring theory

RingEquiv.piUnique

{ι : Type u_7} →
  (R : ι → Type u_8) →
    [inst : Unique ι] → [inst_1 : (i : ι) → NonUnitalNonAssocSemiring (R i)] → ((i : ι) → R i) ≃+* R default

Product of a singleton family of (non-unital non-associative semi)rings is isomorphic to the only member of this family.

Defined in
Mathlib.Algebra.Ring.Equiv
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses Quot.sound
Assumes
UniqueNonUnitalNonAssocSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CommRingCat.coyonedaUnique · cited by 2CommRingCat.coyonedaUniqueIsArtinianRing.isField_of_isReduced_of_isLocalRing · cited by 1IsArtinianRing.isField_of…RingEquiv.piUnique_apply · cited by 0RingEquiv.piUnique_applyRingEquiv.piUnique_symm_apply · cited by 0RingEquiv.piUnique_symm_a…Equiv · cited by 8337EquivRingEquiv · cited by 1147RingEquivNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringUnique · cited by 400UniqueEquiv.piUnique · cited by 4Equiv.piUniqueRingEquiv.piUniqueCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.