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Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$$v^2=1$ are given by the formulajust$v=\pm1$. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula$v=\pm1$. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=1$ are just$v=\pm1$. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1$, for $f$ in the ring. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1$, for $f$ in the ring. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1$. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1 + f\epsilon^{(n+1)/2}$$v=\pm1$, for $f$ in the ring. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1 + f\epsilon^{(n+1)/2}$, for $f$ in the ring. These elements do not span the ring as a vector space over $k$.
Let $k$ be your base field, then consider the ring $k[\epsilon]/\epsilon^{n+1}$. The elements of the ring such that $v^2=0$ are given by the formula $v=\pm1$, for $f$ in the ring. These elements do not span the ring as a vector space over $k$.
