Theorems · Definition · ring theory
LinearAlgebra.FreeProduct.ringCon
{I : Type u} →
[DecidableEq I] →
(R : Type v) →
[inst : CommSemiring R] →
(A : I → Type w) →
[inst_1 : (i : I) → Semiring (A i)] →
[inst_2 : (i : I) → Algebra R (A i)] → RingCon (LinearAlgebra.FreeProduct.FreeTensorAlgebra R A)rel as a ring congruence.
- Defined in
- Mathlib.LinearAlgebra.FreeProduct.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- DirectSumstatement · cited by 446
- RingConstatement · cited by 219
- ringConGenproof · cited by 18
- LinearAlgebra.FreeProduct.FreeTensorAlgebrastatement · cited by 7
- LinearAlgebra.FreeProduct.relproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- LinearAlgebra.FreeProductproof · cited by 11
- LinearAlgebra.FreeProduct.ι'statement · cited by 6
- LinearAlgebra.FreeProduct.liftproof · cited by 5
- LinearAlgebra.FreeProduct.lift_applystatement · cited by 3
- LinearAlgebra.FreeProduct.lof_map_onestatement · cited by 3
- LinearAlgebra.FreeProduct.lofstatement · cited by 1
- LinearAlgebra.FreeProduct.mkAlgHomproof · cited by 1
- LinearAlgebra.FreeProduct.ι_applystatement and proof · cited by 1
- LinearAlgebra.FreeProduct.identify_onestatement and proof · cited by 1
- LinearAlgebra.FreeProduct.lift_comp_ιproof · cited by 0
- LinearAlgebra.FreeProduct.lift_uniqueproof · cited by 0
- LinearAlgebra.FreeProduct.mul_injectionsstatement and proof · cited by 0