Congruence of two-dimensional subspaces in \(M_2(K)\) (characteristic \(\neq 2\))
The structure and classification up to isomorphism of a naturally arising class of local rings is determined. Although the paper is primarily concerned with the case of a finite residue field \(K\), the results apply in fact over any field \(K\) of characteristic \(\neq 2\). The problem is shown to be equivalent to that of classifying two-dimensional subspaces of \(M_2(K)\) up to congruence, and it is in these terms that the question is addressed.
scientific article; zbMATH DE number 1344304