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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$are given by the formula just$v=\pm1$. These elements do not span the ring as a vector space over$k$. 3 deleted 21 characters in body Let$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$in the ring. v=\pm1$. These elements do not span the ring as a vector space over $k$.

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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 $v^2=0$ 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\$.

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