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Theorems · Theorem · group theory

IsUnit.smul_eq_zero

∀ {G : Type u_2} {M : Type u_3} [inst : Monoid G] [inst_1 : AddMonoid M] [inst_2 : DistribMulAction G M] {u : G}
  {x : M}, IsUnit u → (u • x = 0 ↔ x = 0)
Defined in
Mathlib.Algebra.GroupWithZero.Action.Units
Cited by
2 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice
Assumes
MonoidAddMonoidDistribMulAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgEquiv.eq_linearEquivConjAlgEquiv · cited by 4AlgEquiv.eq_linearEquivCo…QuadraticMap.radical_eq_ker_polarBilin · cited by 3QuadraticMap.radical_eq_k…Monoid · cited by 3887MonoidAddMonoid · cited by 2864AddMonoidIsUnit · cited by 1602IsUnitDistribMulAction · cited by 584DistribMulActionIsUnit.unit · cited by 252IsUnit.unitsmul_eq_zero_iff_eq · cited by 4smul_eq_zero_iff_eqIsUnit.smul_eq_zeroCITED BYCITES

Cites6

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Cited by2

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