Theorems · Theorem · commutative algebra
Module.Flat.torsion_eq_bot
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Flat R M],
Submodule.torsion R M = ⊥Flat modules have no torsion.
- Defined in
- Mathlib.RingTheory.Flat.TorsionFree
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- nonZeroDivisorsproof · cited by 895
- smul_zeroproof · cited by 665
- Module.Flatstatement and proof · cited by 279
- eq_bot_iffproof · cited by 159
- Submodule.torsionstatement and proof · cited by 15
- Module.Flat.isSMulRegular_of_nonZeroDivisorsproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Module.Flat.flat_iff_torsion_eq_bot_of_isBezoutproof · cited by 1