Group- ring
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Group- ring
If \(\displaystyle{G}\) is a cyclic group of order \(\displaystyle{|G|=n\in\mathbb{N}}\) and
\(\displaystyle{\mathbb{K}}\) is a field,
then show that
\(\displaystyle{\mathbb{K}[G]\simeq \mathbb{K}[x]/I\,\,\,\,,I=\langle{x^n-1\rangle}}\) .
\(\displaystyle{\mathbb{K}}\) is a field,
then show that
\(\displaystyle{\mathbb{K}[G]\simeq \mathbb{K}[x]/I\,\,\,\,,I=\langle{x^n-1\rangle}}\) .
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