Theorems · Theorem · commutative algebra
Ideal.mem_of_dvd
∀ {α : Type u} {a b : α} [inst : CommSemiring α] (I : Ideal α), a ∣ b → a ∈ I → b ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.mul_mem_rightproof · cited by 71
Cited by7
Results whose statement or proof uses this declaration.
- Valuation.Integers.isPrincipal_iff_exists_isGreatestproof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- Ideal.spanNorm_le_comapproof · cited by 1
- Valuation.Integers.isPrincipal_iff_exists_eq_setOfPred_valuation_leproof · cited by 1
- NumberField.exists_not_isUnramifiedAt_int_of_isGaloisproof · cited by 0
- AlgHom.IsArithFrobAt.apply_of_pow_eq_oneproof · cited by 0
- StandardEtalePair.existsUnique_hasMap_of_hasMap_quotient_of_sq_eq_botproof · cited by 0