 Finiteness criterion for an Artinian local ring (source code)

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= Finiteness criterion for an Artinian local ring
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An Artinian local ring is a finite set exactly when its residue field is finite. If $\mathfrak m^r=0$, each layer $\mathfrak m^i/\mathfrak m^{i+1}$ is a finite-dimensional vector space over that residue field.

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