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Let M be the module over Z [i] generated by elements x, y whose relations are determined by $(1+i)x+(2-i)y=0$ and $3x+5y=0$. How can one write M as a direct sum of cyclic modules?

rschwieb
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Mike Hawk
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    Hey, and welcome to M.SE! To help you, it is helpful to know what you have tried, what your background is (e.g., are you comfortable with the notion of direct sum and cyclic module?), and what your process of thinking was when you approached this question. – Lukas Juhrich Dec 01 '18 at 20:42
  • @Luke, I'm learning modules for the first time. So that, when I think of a module I'm always with the generalization of a vector space. When I think of direct sum I always think on the linear combination of linearly independent generators of subspaces. But I don't know how can I relate this thinking with that question. – Mike Hawk Dec 01 '18 at 22:29
  • @MikeHawk you seem to have confused the title field for the tags field. I changed the title to be more useful. You should do something like that next time. Remember, the goal is to be informative and searchable. If you don’t, well, you’ll probably find out what the consequences are. Good luck. – rschwieb Dec 02 '18 at 00:43
  • Thank you @rschwieb – Mike Hawk Dec 02 '18 at 00:56
  • Similar to these: 1, 2, 3 – Viktor Vaughn Dec 02 '18 at 08:39
  • Thanks @André3000, but could you answer to the question to give me an insight? – Mike Hawk Dec 02 '18 at 10:15

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