Theorems · Definition · commutative algebra
MvPowerSeries.truncTotalAlgHom
(σ : Type u_3) →
(R : Type u_4) →
[Finite σ] →
[inst : CommRing R] →
(n : ℕ) → MvPowerSeries σ R →ₐ[MvPolynomial σ R] MvPolynomial σ R ⧸ MvPolynomial.idealOfVars σ R ^ nThe canonical map induced by truncTotal from multivariate power series to
the quotient ring of multivariate polynomials by the n-th power of
the ideal spanned by all variables.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Equiv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finsuppstatement · cited by 5,255
- Idealstatement · cited by 4,748
- AlgHomstatement · cited by 3,236
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement · cited by 2,301
- MvPolynomialstatement and proof · cited by 2,140
- MvPowerSeriesstatement and proof · cited by 659
- Ideal.Quotient.mkproof · cited by 610
- MvPowerSeries.truncTotalproof · cited by 28
- MvPolynomial.idealOfVarsstatement and proof · cited by 21
Cited by4
Results whose statement or proof uses this declaration.
- MvPowerSeries.toAdicCompletionproof · cited by 5
- MvPowerSeries.truncTotalAlgHom_applystatement and proof · cited by 1
- MvPowerSeries.truncTotalAlgHom.congr_simpstatement and proof · cited by 0
- MvPowerSeries.toAdicCompletion_coeproof · cited by 0