= Gelfand–Kirillov dimension
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{title2=$\operatorname{GKdim}A$}
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= GK dimension
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For a nonzero finitely generated <algebra> over a <field>, choose a finite-dimensional generating <vector subspace> $V$ containing $1$. The dimension is $\operatorname{GKdim}A=\limsup_{n\to\infty}\log(\dim_kV^n)/\log n$. Changing $V$ only rescales the filtration index by bounded factors. A nonzero finite-dimensional <algebra> has dimension zero; a <polynomial ring> in $r$ variables has dimension $r$. The zero <algebra> is often assigned dimension $-\infty$.
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