Theorems · Theorem · commutative algebra
Int.cast_mem_ideal_iff
∀ {R : Type u_1} [inst : Ring R] {I : Ideal R} {d : ℤ}, ↑d ∈ I ↔ ↑(Ideal.absNorm (Ideal.under ℤ I)) ∣ d- Defined in
- Mathlib.RingTheory.Ideal.Int
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- MonoidWithZeroHomstatement · cited by 704
- Ideal.understatement and proof · cited by 170
- eq_intCastproof · cited by 127
- Ideal.absNormstatement · cited by 123
- Ideal.mem_span_singletonproof · cited by 69
- Ideal.mem_comapproof · cited by 54
- Ideal.under_defproof · cited by 15
- Int.ideal_span_absNorm_eq_selfproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Int.absNorm_under_eq_sInfproof · cited by 2
- Int.absNorm_under_memproof · cited by 1
- Ideal.ringChar_quotproof · cited by 0