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Similarity of Matrices Over Local Rings of Length Two

Prasad, Amritanshu and Singla, Pooja and Spallone, Steven (2015) Similarity of Matrices Over Local Rings of Length Two. In: INDIANA UNIVERSITY MATHEMATICS JOURNAL, 64 (2). pp. 471-514.

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Official URL: http://www.researchgate.net/publication/256238721_...

Abstract

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the INDIANA UNIV MATH JOURNAL, SWAIN HALL EAST 222, BLOOMINGTON, IN 47405 USA
Keywords: Similarity classes; matrices; local rings; extensions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 19 Nov 2015 04:57
Last Modified: 19 Nov 2015 04:57
URI: http://eprints.iisc.ac.in/id/eprint/52787

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