Theorems · Definition · commutative algebra
MvPolynomial.coeffsIn
{R : Type u_2} →
{S : Type u_3} →
(σ : Type u_4) →
[inst : CommSemiring R] →
[inst_1 : CommSemiring S] → [inst_2 : Module R S] → Submodule R S → Submodule R (MvPolynomial σ S)The R-submodule of multivariate polynomials whose coefficients lie in an R-submodule M.
- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
Cited by18
Results whose statement or proof uses this declaration.
- MvPolynomial.C_mem_coeffsInstatement · cited by 1
- MvPolynomial.mul_monomial_mem_coeffsInstatement · cited by 1
- MvPolynomial.monomial_mem_coeffsInstatement · cited by 1
- ChevalleyThm.chevalley_mvPolynomialCstatement and proof · cited by 1
- MvPolynomial.le_coeffsIn_powstatement and proof · cited by 1
- MvPolynomial.mem_coeffsIn_iff_coeffs_subsetstatement · cited by 1
- MvPolynomial.coeffsIn_eq_span_monomialstatement and proof · cited by 1
- MvPolynomial.coeffsIn_lestatement · cited by 1
- MvPolynomial.coeffsIn_powstatement · cited by 1
- MvPolynomial.mul_X_mem_coeffsInstatement · cited by 0
- MvPolynomial.coe_coeffsInstatement and proof · cited by 0
- chevalley_mvPolynomial_mvPolynomialproof · cited by 0