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Zbl 1176.15013
Avni, Nir; Onn, Uri; Prasad, Amritanshu; Vaserstein, Leonid
Similarity classes of $3 \times 3$ matrices over a local principal ideal ring.
(English)
[J] Commun. Algebra 37, No. 8, 2601-2615 (2009). ISSN 0092-7872; ISSN 1532-4125/e

In general, the classification problem of similarity classes in $n$ by $n$ matrices over rings other than fields is a highly nontrivial question. In this article, similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.
[Sheng Chen (Harbin)]
MSC 2000:
*15A21 Canonical forms, etc.
15A54 Matrices over function rings
15A33 Matrices over special rings

Keywords: enumeration; classification; similarity classes; local principal ideal commutative ring; generating function

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