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Math Help - modules that are both injective projective

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    modules that are both injective projective

    Vector spaces are both projective and injective if the axiom of choice holds. Are there any other modules with this property? Do they have a good characterization?
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    Re: modules that are both injective projective

    Quote Originally Posted by ymar View Post
    Vector spaces are both projective and injective if the axiom of choice holds. Are there any other modules with this property? Do they have a good characterization?
    there's a characterization of rings over which every module is both projective and injective. these rings are called semisimple and they are in the form \bigoplus_{i=1}^k M_{n_i}(D_i), where k \geq 1 is any integer, each D_i is a division ring and M_{n_i}(D_i) is the ring of n_i \times n_i matrices with entries in D_i.
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