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Theorems · Theorem · commutative algebra

ratCast_smul_eq

∀ {E : Type u_3} (R : Type u_4) (S : Type u_5) [inst : AddCommGroup E] [inst_1 : DivisionRing R]
  [inst_2 : DivisionRing S] [inst_3 : Module R E] [inst_4 : Module S E] (r : ℚ) (x : E), ↑r • x = ↑r • x

If E is a vector space over two division rings R and S, then scalar multiplications agree on rational numbers in R and S.

Defined in
Mathlib.Algebra.Module.Rat
Cited by
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Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupDivisionRingDivisionRingModuleModule
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Module · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupDivisionRing · cited by 1062DivisionRingAddMonoidHom.id · cited by 107AddMonoidHom.idmap_ratCast_smul · cited by 4map_ratCast_smulratCast_smul_eqCITED BYCITES

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