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Theorems · Theorem · commutative algebra

IsSMulRegular.not_zero

∀ {R : Type u_1} {M : Type u_3} [inst : MonoidWithZero R] [inst_1 : Zero M] [inst_2 : MulActionWithZero R M]
  [nM : Nontrivial M], ¬IsSMulRegular M 0

The 0 element is not M-regular, on a non-trivial module.

Defined in
Mathlib.Algebra.Regular.SMul
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidWithZeroZeroMulActionWithZeroNontrivial
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Around this declaration

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

AddCircle.finite_torsion_of_isSMulRegular_int · cited by 2AddCircle.finite_torsion_…AddCircle.finite_torsion_of_isSMulRegular · cited by 1AddCircle.finite_torsion_…Nontrivial · cited by 2416NontrivialMonoidWithZero · cited by 456MonoidWithZeroIsSMulRegular · cited by 128IsSMulRegularMulActionWithZero · cited by 79MulActionWithZeroIsSMulRegular.not_zero_iff · cited by 1IsSMulRegular.not_zero_iffIsSMulRegular.not_zeroCITED BYCITES

Cites5

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Cited by2

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