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- - **If D is a division ring, why are D-mods semisimple?**
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If D is a division ring, why are D-mods semisimple?Let D be a division ring. Why must every D-module be semisimple? |

Re: If D is a division ring, why are D-mods semisimple?If is a field, why must every -module (ie vector space) be semisimple? What are the irreducible -modules? |

Re: If D is a division ring, why are D-mods semisimple?if D is a division ring, then a D-module is free (it satisfies, for example, all the usual axioms of a vector space). in particular, division rings have the invariant basis number property. we can thus regard any D-module M as a direct sum: where: since D is a division ring, it has no non-trivial proper D-submodules (which would necessarily be non-trivial proper ideals of D). this is because every element of D-{0} is a unit. |

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