Theorems · Theorem · commutative algebra
IsIntegral.sum
∀ {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
- 10 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.sumstatement · cited by 5,195
- IsIntegralstatement and proof · cited by 427
- integralClosureproof · cited by 105
- Subalgebra.sum_memproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- IsIntegral.detproof · cited by 3
- PowerBasis.repr_gen_pow_isIntegralproof · cited by 2
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- Polynomial.isIntegral_coeff_prodproof · cited by 1
- Polynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- PowerBasis.repr_mul_isIntegralproof · cited by 1
- PowerBasis.toMatrix_isIntegralproof · cited by 1
- mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- isIntegral_discr_mul_of_mem_traceDualproof · cited by 0