Which rings are subrings of matrix rings?

Discussion in 'Math Research' started by Kevin Buzzard, Sep 20, 2009.

  1. In this post all rings are commutative with a 1, unless we explicitly say
    so, and all morphisms of rings send 1 to 1.

    Let A be a Noetherian local integral domain. Let T be a non-zero A-algebra
    which, as an A-module, is finitely-generated and torsion-free.

    Can one realise T as a subring of the (not necessarily commutative)
    ring End_A(A^n) for some n>=1?

    Kevin
     
    Kevin Buzzard, Sep 20, 2009
    #1
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