= Gelfand–Kirillov dimension of a module
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{title2=$\operatorname{GKdim}_AM$}
= GK dimension of a module
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{synonym}
For a nonzero right <module> $M$ that is a <finitely generated module>, choose a finite-dimensional generating <vector subspace> $W$ and define $\operatorname{GKdim}_AM=\limsup_{n\to\infty}\log(\dim_kWV^n)/\log n$, where $V$ generates the <algebra> and contains $1$. For a left <module> use $V^nW$. It is independent of these choices and measures polynomial-order growth of a generating <filtration of a module>.
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