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is a field if and only if $p(x)$ is an irreducible polynomial.  \end{Theorem}  \begin{Example}  \textbf{Nota (M)}: non capisco cosa intendi comunicare con l'esempio...  Let $\Fb[x]$ where $x^2+x+1=0$, that is $x^2=x+1$. The set of polynomials are $\{0,1,x,x+1\}$. The inverse of $1$ is $1$, the inverse of $x$ is $x+1$. In fact $x(x+1)=x^2+x=x+1+x=1$.  Let $\Fb[x]$ where $x^2=0$. The set of polynomials are $\{0,1,x,x+1\}$. The inverse of $x$ this time does not exist.