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Z -module Question

  1. Dec 8, 2008 #1
    Z-module Question

    Let [tex]M[/tex] be the [tex]\mathbb{Z}[/tex]-module generated by the elements [tex]v_1[/tex], [tex]v_2[/tex] such that [tex](1+i)v_1+(2-i)v_2=0[/tex] and [tex]3v_1+5iv_2=0[/tex]. Find an integer [tex]r \geq 0[/tex] and a torsion [tex]\mathbb{Z}[/tex]-module [tex]T[/tex] such that [tex]M \cong \mathbb{Z}^r \times T[/tex].
  2. jcsd
  3. Dec 8, 2008 #2
    Re: Z-module Question

    Can you find the torsion submodule? After that, Zr should be isomorphic to M/T.
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