Theorems · Theorem · commutative algebra
FractionalIdeal.eq_one_div_of_mul_eq_one_right
∀ {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 J : FractionalIdeal (nonZeroDivisors R₁) K),
I * J = 1 → J = 1 / I- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement and proof · cited by 423
- mul_le_mul'proof · cited by 274
- Units.extproof · cited by 86
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.one_div_spanSingletonproof · cited by 2
- FractionalIdeal.right_inverse_eqproof · cited by 2
- FractionalIdeal.mul_div_self_cancel_iffproof · cited by 1