Theorems · Theorem · commutative algebra
IsIntegral.prod
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {α : Type u_5}
{s : Finset α} (f : α → A), (∀ x ∈ s, IsIntegral R (f x)) → IsIntegral R (∏ x ∈ s, f x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Finset.prodstatement · cited by 2,356
- IsIntegralstatement and proof · cited by 427
- integralClosureproof · cited by 105
- Subalgebra.prod_memproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsIntegral.detproof · cited by 3
- RingOfIntegers.dvd_normproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1