Abstract

The structure and classification up to isomorphism of a naturally arising class of local rings is determined. Although we are primarily interested in the case of a finite residue field K, our results apply in fact over any field K of characteristic ≠2. The problem is shown to be equivalent to that of classifying two-dimensional subspaces of M₂(K) up to congruence, and it is in these terms that the question is addressed.

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