Theorems · Theorem · commutative algebra
PolynomialModule.coeff_single
∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (n : ℕ) (m : M),
(PolynomialModule.single R n m).coeff = fun₀ | n => m- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 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.
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Finsuppstatement · cited by 5,255
- Finsupp.singlestatement · cited by 943
- PolynomialModule.singlestatement · cited by 31
- PolynomialModule.coeffstatement · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.Filtration.submodule_eq_span_le_iff_stable_geproof · cited by 1
- Ideal.Filtration.submodule_closure_singleproof · cited by 1
- PolynomialModule.single_applyproof · cited by 0