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Theorems · Definition · ring theory

Bialgebra.Quotient.comulAlgHom

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : Ring A] →
        [inst_2 : Bialgebra R A] →
          (I : Ideal A) →
            [inst_3 : I.IsTwoSided] →
              [(Submodule.restrictScalars R I).IsCoideal] → A ⧸ I →ₐ[R] TensorProduct R (A ⧸ I) (A ⧸ I)

The comultiplication on A ⧸ I, as an R-algebra homomorphism.

Defined in
Mathlib.RingTheory.Bialgebra.Quotient
Cited by
2 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingBialgebraIdeal.IsTwoSidedSubmodule.IsCoideal
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Bialgebra.Quotient.comulAlgHom.congr_simp · cited by 0comulAlgHom.congr_simpBialgebra.Quotient.comul_comp_mkₐ · cited by 0Quotient.comul_comp_mkₐCommRing · cited by 17173CommRingRing · cited by 7463RingIdeal · cited by 4748IdealAlgHom · cited by 3236AlgHomTensorProduct · cited by 2545TensorProductHasQuotient.Quotient · cited by 2301HasQuotient.QuotientAlgHom.comp · cited by 501AlgHom.compSubmodule.restrictScalars · cited by 180Submodule.restrictScalarsIdeal.IsTwoSided · cited by 179Ideal.IsTwoSidedBialgebra · cited by 160BialgebraIdeal.Quotient.mkₐ · cited by 101Quotient.mkₐAlgebra.TensorProduct.map · cited by 97TensorProduct.mapBialgebra.comulAlgHom · cited by 20Bialgebra.comulAlgHomSubmodule.IsCoideal · cited by 17Submodule.IsCoidealIdeal.Quotient.liftₐ · cited by 15Quotient.liftₐQuotient.comulAlgHomCITED BYCITES

Cites15

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Cited by2

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