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"Let $GR=(s,sm)$" the Galois Ring with characteristic $p^s$ and $p^{sm}$ elements. If $n\mid m$ then exists $R_0=GR(s,sn)$ a Galois Ring that contains $R$ as a subring".

I've already seen that this theorem has already asked before, but there isn't an answer yet.

"Let $GR=(s,sm)$" the Galois Ring with characteristic $p^s$ and $p^{sm}$ elements. The construction of Galois rings that I'm using is the following:

Let $\mathbb{Z}_{p^s}[x]$ the polynomial ring on the indeterminate "x" and coefficients on $\mathbb{Z}_{p^s}$ and we define the concept of monic basic irreducible polynomial (or primitive) $h(x)$ as follows.

Let $h(x)\in\mathbb{Z}_{p^s}[x]$ a polynomial of degree "$m$". We say that "$h$" are a monic basic irreducible polynomial (or primitive) if the polynomial $h_0(x)\in\mathbb{F}_p[x]$ is monic and irreducible (or primitive) on $\mathbb{F}_p[x]$. The polynomial $h_0(x)$ is the polynomial constructed by taking the reduction modulo $p$ of the coefficients of $h(x)$.

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