Theorems · Definition · commutative algebra
PolynomialModule.comp
{R : Type u_2} →
{M : Type u_3} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Polynomial R → PolynomialModule R M →ₗ[R] PolynomialModule R Mcomp p q is the composition of p : R[X] and q : M[X] as q(p(x)).
- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- LinearMap.compproof · cited by 1,642
- LinearMap.restrictScalarsproof · cited by 215
- PolynomialModulestatement · cited by 76
- PolynomialModule.evalproof · cited by 17
- PolynomialModule.lsingleproof · cited by 12
- PolynomialModule.mapproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- taylorWithinEval_succproof · cited by 6
- PolynomialModule.comp_applystatement and proof · cited by 3
- taylorWithinproof · cited by 2
- PolynomialModule.comp_evalstatement and proof · cited by 1
- PolynomialModule.comp_singlestatement · cited by 1
- taylorWithin_succstatement and proof · cited by 1
- PolynomialModule.comp_smulstatement and proof · cited by 0