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Michela Ceria edited section_Bytes_The_polynomials_in__.tex
about 6 years ago
Commit id: a1b50f8ced271ae8c36d0608ab2192b4ebcba309
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\begin{itemize}
\item[i)] $A_1$ is an abelian group w.r.t. the sum of polynomials;
\item[ii)] $A_1\setminus\{0\}=\{1,x,x+1\}$ is an abelian group w.r.t. the product of polynomials;
\item[iii)] $(f+g)\cdot h=fh+gh$, for any $f,g,h \in
A$. A_1$.
\end{itemize}
Since $A_1$ is formed by polynomials, properties i) and iii) are obvious.
As regards ii), we need only to prove that each nonzero element in $A_1$ has an inverse: