Theorems · Theorem · commutative algebra
FractionalIdeal.le_self_mul_one_div
∀ {R₁ : Type u_3} [inst : CommRing R₁] {K : Type u_4} [inst_1 : Field K] [inst_2 : Algebra R₁ K]
[inst_3 : IsFractionRing R₁ K] [inst_4 : IsDomain R₁] {I : FractionalIdeal (nonZeroDivisors R₁) K},
I ≤ 1 → I ≤ I * (1 / I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_reflproof · cited by 2,061
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmoduleproof · cited by 130
- FractionalIdeal.coe_mulproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.le_self_mul_invproof · cited by 1