The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence
The $(z,k)$--equivalence of matrices over imaginary Euclidean
quadratic rings is investigated. The classes of matrices over
these rings are selected for which the standard form with respect
to $(z,k)$--equivalence is uniquely defined and equal to the Smith
normal form. It is established that the number of standard forms
over imaginary Euclidean quadratic rings is finite. Bounds for a
number of standard forms are established.
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