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Theorems · Theorem · commutative algebra

IsSMulRegular.subsingleton

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

The element 0 is M-regular if and only if M is trivial.

Defined in
Mathlib.Algebra.Regular.SMul
Cited by
1 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
MonoidWithZeroZeroMulActionWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsSMulRegular.zero_iff_subsingleton · cited by 2IsSMulRegular.zero_iff_su…MonoidWithZero · cited by 456MonoidWithZeroIsSMulRegular · cited by 128IsSMulRegularMulActionWithZero · cited by 79MulActionWithZeroMulActionWithZero.zero_smul · cited by 2MulActionWithZero.zero_sm…IsSMulRegular.subsingletonCITED BYCITES

Cites4

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Cited by1

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