Theorems · Theorem · commutative algebra
Ideal.isUnit_iff
∀ {R : Type u} [inst : CommSemiring R] {I : Ideal R}, IsUnit I ↔ I = ⊤See also isUnit_iff_eq_one.
- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- IsUnitstatement · cited by 1,602
- eq_top_iffproof · cited by 236
- Ideal.one_eq_topproof · cited by 83
- Ideal.mul_topproof · cited by 42
- isUnit_iff_dvd_oneproof · cited by 21
- Ideal.le_of_dvdproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.prime_of_isPrimeproof · cited by 15
- IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_oneproof · cited by 4
- IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizerproof · cited by 3
- Ideal.pow_right_strictAntiproof · cited by 2
- Ideal.pow_succ_lt_powproof · cited by 2
- Ideal.squarefree_span_singletonproof · cited by 0
- cardQuot_mulproof · cited by 0