Theorems · Theorem · commutative algebra
PolynomialModule.monomial_smul_lsingle
∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (i : ℕ) (r : R)
(j : ℕ) (m : M),
(Polynomial.monomial i) r • (PolynomialModule.lsingle R j) m = (PolynomialModule.lsingle R (i + j)) (r • m)- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites11
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- DFunLike.coestatement · cited by 62,936
- 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 · cited by 5,681
- Polynomial.monomialstatement · cited by 256
- PolynomialModulestatement · cited by 76
- PolynomialModule.lsinglestatement · cited by 12
- PolynomialModule.monomial_smul_singleproof · cited by 6
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