Theorems · Definition · commutative algebra
PolynomialModule.equivPolynomialSelf
{R : Type u_2} → [inst : CommRing R] → PolynomialModule R R ≃ₗ[Polynomial R] Polynomial RPolynomialModule R R is isomorphic to R[X] as an R[X] module.
- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- LinearEquivstatement · cited by 3,317
- AddEquivproof · cited by 1,087
- RingEquiv.symmproof · cited by 567
- AddEquiv.symmproof · cited by 530
- Equiv.toFunproof · cited by 279
- AddEquiv.toEquivproof · cited by 174
- Equiv.invFunproof · cited by 163
- PolynomialModulestatement and proof · cited by 76
- AddEquiv.transproof · cited by 53
Cited by5
Results whose statement or proof uses this declaration.
- Differential.mapCoeffsproof · cited by 7
- Differential.mapCoeffs_monomialproof · cited by 2
- Polynomial.Bivariate.pderiv_zero_equivMvPolynomialstatement and proof · cited by 1
- PolynomialModule.equivPolynomialSelf_apply_eqstatement · cited by 0
- StandardEtalePresentation.toSubmersivePresentation_jacobianproof · cited by 0