Let $M$ be a Noetherian and Artinian module. Suppose that: $\bigoplus_{i=1}^{q} A_{i} \oplus \bigoplus_{i=1}^{t} B_{i} \cong \bigoplus_{i=1}^{q} A_{i} \oplus \bigoplus_{i=1}^{r} C_{i}$
where all $A_{i},B_{i},C_{i}$ are indecomposable submodules of $M$.
Can we always guarantee that $B_{i} \cong C_{i}$ for all $i \in \{1,2,...,t\}$? That is, can we "cancel" the term $\displaystyle\bigoplus_{i=1}^{q} A_{i}$?