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Theorems · Theorem · commutative algebra

PolynomialModule.coeff_inj

∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {x y : PolynomialModule R M}, x.coeff = y.coeff ↔ x = y
Defined in
Mathlib.Algebra.Polynomial.Module.Basic
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
CommRingAddCommGroupModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PolynomialModule.ext · cited by 4PolynomialModule.extPolynomialModule.coeff_eq_zero · cited by 0PolynomialModule.coeff_eq…Module · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupFinsupp · cited by 5255FinsuppPolynomialModule · cited by 76PolynomialModulePolynomialModule.coeff · cited by 27PolynomialModule.coeffPolynomialModule.coeff_injective · cited by 1PolynomialModule.coeff_in…PolynomialModule.coeff_injCITED BYCITES

Cites7

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Cited by2

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