Theorems · Theorem · commutative algebra
DividedPowerAlgebra.map_apply
∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (S : Type u_4)
[inst_3 : CommSemiring S] {N : Type u_5} [inst_4 : AddCommMonoid N] [inst_5 : Module R N] [inst_6 : Module S N]
(f : M →ₗ[R] N) [inst_7 : Algebra R S] [inst_8 : IsScalarTower R S N] {p : MvPolynomial (ℕ × M) R},
(DividedPowerAlgebra.map S f) ↑p = (MvPolynomial.aeval fun nm => DividedPowerAlgebra.dp S nm.1 (f nm.2)) p- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement · cited by 5,255
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.aevalstatement and proof · cited by 298
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