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Theorems · Theorem · group theory

IsScalarTower.smul_assoc

∀ {M : Type u_9} {N : Type u_10} {α : Type u_11} {inst : SMul M N} {inst_1 : SMul N α} {inst_2 : SMul M α}
  [self : IsScalarTower M N α] (x : M) (y : N) (z : α), (x • y) • z = x • y • z

Associativity of •

Defined in
Mathlib.Algebra.Group.Action.Defs
Cited by
10 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
IsScalarTower
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

smul_assoc · cited by 150smul_assocIsScalarTower.algebraMap_eq · cited by 110IsScalarTower.algebraMap_…IsScalarTower.algebraMap_smul · cited by 19IsScalarTower.algebraMap_…IsScalarTower.to₁₃₄ · cited by 5IsScalarTower.to₁₃₄Submodule.span_smul_of_span_eq_top · cited by 3Submodule.span_smul_of_sp…IsIntegralClosure.isTorsionFree · cited by 2IsIntegralClosure.isTorsi…IsScalarTower.to₁₂₄ · cited by 2IsScalarTower.to₁₂₄Submodule.smul_mem_span_smul_of_mem · cited by 0Submodule.smul_mem_span_s…IsScalarTower.to₁₂₃ · cited by 0IsScalarTower.to₁₂₃IsScalarTower.to₂₃₄ · cited by 0IsScalarTower.to₂₃₄IsScalarTower · cited by 3896IsScalarTowerIsScalarTower.smul_assocCITED BYCITES

Cites1

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Cited by10

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