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Theorems · Theorem · commutative algebra

IsRegular.isSMulRegular

∀ {R : Type u_1} {M : Type u_3} {inst : Semiring R} {inst_1 : AddCommMonoid M} {inst_2 : Module R M}
  [self : Module.IsTorsionFree R M] ⦃r : R⦄, IsRegular r → IsSMulRegular M r

Alias of Module.IsTorsionFree.isSMulRegular.

Defined in
Mathlib.Algebra.Module.Torsion.Free
Cited by
6 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
Module.IsTorsionFree
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Around this declaration

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

Function.Injective.moduleIsTorsionFree · cited by 4Injective.moduleIsTorsion…IsRegular.smul_right_injective · cited by 2IsRegular.smul_right_inje…Module.IsTorsionFree.comap · cited by 1IsTorsionFree.comapIsLocalizedModule.isTorsionFree_of_forall_isRegular · cited by 1IsLocalizedModule.isTorsi…Module.IsTorsionFree.trans · cited by 0IsTorsionFree.transIsSMulRegular.of_ne_zero · cited by 0IsSMulRegular.of_ne_zeroModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidModule.IsTorsionFree · cited by 600Module.IsTorsionFreeIsSMulRegular · cited by 128IsSMulRegularIsRegular · cited by 116IsRegularModule.IsTorsionFree.isSMulRegular · cited by 1IsTorsionFree.isSMulRegul…IsRegular.isSMulRegularCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.