Theorems · Theorem · commutative algebra
Ideal.sum_mem
∀ {α : Type u} [inst : Semiring α] (I : Ideal α) {ι : Type u_1} {t : Finset ι} {f : ι → α},
(∀ c ∈ t, f c ∈ I) → ∑ i ∈ t, f i ∈ I- Defined in
- Mathlib.RingTheory.Ideal.BigOperators
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement · cited by 5,195
- Idealstatement and proof · cited by 4,748
- Submodule.sum_memproof · cited by 42
Cited by19
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_idealproof · cited by 4
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memproof · cited by 3
- Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_selfproof · cited by 3
- MvPolynomial.toMvPowerSeries_uniformContinuousproof · cited by 2
- Ideal.le_toIdeal_homogeneousHullproof · cited by 2
- Algebra.FinitePresentation.of_span_eq_top_targetproof · cited by 2
- Polynomial.IsWeaklyEisensteinAt.mulproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1
- Ideal.homogeneous_spanproof · cited by 1
- PowerSeries.eq_of_le_of_X_notMem_of_fg_of_isPrimeproof · cited by 1
- ProjectiveSpectrum.basicOpen_eq_union_of_projectionproof · cited by 1
- Ideal.isOka_fgproof · cited by 1