Let $G=\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4=\mathbb{Z}_4^4$ be a direct product of $4$ copies of the the cyclic group $\mathbb{Z}_4$ of order $4$. Can one regards $G$ as a vector space of dimension $4$ over the ring $\mathbb{Z}_4$ or can it only be regarded as a $4$-dimensional module over $\mathbb{Z}_4$?
2026-03-28 20:14:57.1774728897
A direct product $G=\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4\times\mathbb{Z}_4$ of the cyclic group $\mathbb{Z}_4$ of order $4$.
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