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Theorems · Theorem · commutative algebra

IsSMulRegular.of_map

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {a : R} [inst : SMul R M] [inst_1 : SMul S M] (f : R → S),
  (∀ (m : M), f a • m = a • m) → IsSMulRegular M (f a) → IsSMulRegular M a

Alias of the forward direction of isSMulRegular_map.

Defined in
Mathlib.Algebra.Regular.SMul
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses propext, Quot.sound
Assumes
SMulSMul
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Around this declaration

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

Module.IsTorsionFree.comap · cited by 1IsTorsionFree.comapIsSMulRegular · cited by 128IsSMulRegularisSMulRegular_map · cited by 2isSMulRegular_mapIsSMulRegular.of_mapCITED BYCITES

Cites2

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

Cited by1

Results whose statement or proof uses this declaration.