Theorems · Theorem · commutative algebra
Submodule.finiteQuotient_iff
∀ {M : Type u_3} [inst : AddCommGroup M] [Module.Free ℤ M] [Module.Finite ℤ M] (N : Submodule ℤ M),
Finite (M ⧸ N) ↔ Module.finrank ℤ ↥N = Module.finrank ℤ M- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- Module.finrankstatement and proof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- Nat.cardproof · cited by 844
- Module.Freestatement and proof · cited by 597
- natCast_zsmulproof · cited by 118
- Submodule.toAddSubgroupproof · cited by 106
- AddSubgroup.indexproof · cited by 104
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1