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ISRN Algebra
Volume 2012 (2012), Article ID 520148, 9 pages
http://dx.doi.org/10.5402/2012/520148
Research Article

Cogredient Standard Forms of Symmetric Matrices over Galois Rings of Odd Characteristic

School of Sciences, Shandong University of Technology, Shandong, Zibo 255091, China

Received 20 March 2012; Accepted 13 May 2012

Academic Editors: A. V. Kelarev, D. Kressner, and W. A. Rodrigues

Copyright © 2012 Yonglin Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 𝑅=GR(𝑝𝑠,π‘π‘ π‘š) be a Galois ring of characteristic 𝑝𝑠 and cardinality π‘π‘ π‘š, where 𝑠 and π‘š are positive integers and 𝑝 is an odd prime number. Two kinds of cogredient standard forms of symmetric matrices over 𝑅 are given, and an explicit formula to count the number of all distinct cogredient classes of symmetric matrices over 𝑅 is obtained.