Theorems · Theorem · commutative algebra
IsFractionRing.self_iff_nonZeroDivisors_le_isUnit
∀ {R : Type u_1} [inst : CommRing R], IsFractionRing R R ↔ nonZeroDivisors R ≤ IsUnit.submonoid R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement · cited by 738
- le_antisymm_iffproof · cited by 62
- IsUnit.submonoidstatement and proof · cited by 56
- isUnit_le_nonZeroDivisorsproof · cited by 2
- IsFractionRing.self_iff_nonZeroDivisors_eq_isUnitproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsFractionRing.self_iff_bijectiveproof · cited by 1
- Ideal.IsMaximal.mem_associatedPrimes_of_isFractionRingproof · cited by 0
- Ideal.eq_top_of_mk_tensor_eq_oneproof · cited by 0