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Theorems · Theorem · commutative algebra

IsAddUnit.smul_right

∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {r : R} (x : M),
  IsAddUnit r → IsAddUnit (r • x)
Defined in
Mathlib.Algebra.Module.End
Cited by
3 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidModule
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Around this declaration

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

Matrix.isAddUnit_detp_mul_detp · cited by 1Matrix.isAddUnit_detp_mul…Matrix.isAddUnit_detp_smul_mul_adjp · cited by 0Matrix.isAddUnit_detp_smu…Matrix.detp_smul_adjp · cited by 0Matrix.detp_smul_adjpDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidIsAddUnit · cited by 215IsAddUnitAddMonoidHom.flip · cited by 25AddMonoidHom.flipsmulAddHom · cited by 17smulAddHomIsAddUnit.map · cited by 16IsAddUnit.mapIsAddUnit.smul_rightCITED BYCITES

Cites8

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Cited by3

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