Theorems · Theorem · commutative algebra
Ideal.Quotient.index_eq_zero
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R), ↑(Submodule.toAddSubgroup I).index = 0- Defined in
- Mathlib.Algebra.CharP.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 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.
Cites11
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
- Fintypeproof · cited by 7,736
- Idealstatement and proof · cited by 4,748
- Finiteproof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.cast_zeroproof · cited by 1,870
- Fintype.ofFiniteproof · cited by 255
- Submodule.toAddSubgroupstatement and proof · cited by 106
- AddSubgroup.indexstatement · cited by 104
- Nat.cast_card_eq_zeroproof · cited by 8
- Nat.card_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.absNorm_memproof · cited by 5