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May 8, 2015 at 11:04 comment added Alex B. Yes, I hadn't seen the edit.
May 7, 2015 at 10:55 comment added Todd Leason @Alex B.: I'm talking about Z-irreducible modules in the sense of C-R as should be clear from the reference. Z-irreducible modules are of course indecomposable. The OP explained to be interested in (cyclic) subgroups of GL_n(Z). Therefore only representations arising from Z-free modules are of interest here.
May 4, 2015 at 10:57 comment added Alex B. You mean indecomposable, rather than irreducible. And you are implicitly talking about the $\mathbb{Z}$-free ones.
May 3, 2015 at 16:36 history answered Todd Leason CC BY-SA 3.0