Theorems · Theorem · commutative algebra
Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisors
∀ (R : Type u_1) {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsDomain R]
[Module.IsTorsionFree R M] (m : M), Ideal.torsionOf R M m = ⊥ ↔ m ≠ 0- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Module.IsTorsionFreestatement and proof · cited by 600
- smul_eq_zeroproof · cited by 40
- Submodule.eq_bot_iffproof · cited by 31
- bot_ne_topproof · cited by 24
- Ideal.torsionOfstatement and proof · cited by 14
- Ideal.mem_torsionOf_iffproof · cited by 2
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