# Z -module Question

1. Dec 8, 2008

### mathsss2

Z-module Question

Let $$M$$ be the $$\mathbb{Z}$$-module generated by the elements $$v_1$$, $$v_2$$ such that $$(1+i)v_1+(2-i)v_2=0$$ and $$3v_1+5iv_2=0$$. Find an integer $$r \geq 0$$ and a torsion $$\mathbb{Z}$$-module $$T$$ such that $$M \cong \mathbb{Z}^r \times T$$.

2. Dec 8, 2008