Theorems · Theorem · commutative algebra
Module.exists_isPrincipal_quotient_of_finite
∀ (R : Type u_1) (M : Type u_2) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Finite R M] [Nontrivial M], ∃ N, N ≠ ⊤ ∧ ⊤.IsPrincipal
- Defined in
- Mathlib.RingTheory.TensorProduct.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
Cited by1
Results whose statement or proof uses this declaration.
- Module.exists_surjective_quotient_of_finiteproof · cited by 0