Originally Posted by

**badgerigar** I want to know how to find the invariant factor decompostion of

$\displaystyle M \cong \frac{R}{((x-1)^3)}\oplus \frac{R}{((x^2+1)^2)} \oplus \frac{R}{((x-1)(x^2+1)^4)} \oplus\frac{R}{((x+2)(x^2+1)^2)}$

If it is relevant, in a previous part of the question I found the primary decomposition to be

$\displaystyle

\frac{R}{((x-1)^3)} \oplus \frac{R}{((x^2+1)^2)} \oplus \frac{R}{(x-1)} \oplus \frac{R}{((x^2+1)^4)} \oplus \frac{R}{(x+2)} \oplus \frac{R}{((x^2+1)^2)}$

edit: forgot to mention that $\displaystyle R = \mathbb{R}[x]$