Theorems · Theorem · commutative algebra
Submodule.cardQuot_eq_one_iff
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {P : Submodule R M},
P.cardQuot = 1 ↔ P = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Submodule.neg_memproof · cited by 31
- Submodule.cardQuotstatement · cited by 14
- AddSubgroup.index_eq_oneproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.absNorm_eq_one_iffproof · cited by 4