Theorems · Theorem · commutative algebra
Ideal.torsionOf_zero
∀ (R : Type u_1) (M : Type u_2) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], Ideal.torsionOf R M 0 = ⊤
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- Idealstatement · cited by 4,748
- LinearMap.kerproof · cited by 848
- Ideal.torsionOfstatement · cited by 14
- LinearMap.ker_zeroproof · cited by 12
- LinearMap.toSpanSingleton_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisorsproof · cited by 0
- Ideal.torsionOf_eq_top_iffproof · cited by 0