Congruence of symmetric matrices over local rings

被引:2
作者
Cao, Yonglin [2 ]
Szechtman, Fernando [1 ]
机构
[1] Univ Regina, Dept Math & Stat, Saskatoon, SK, Canada
[2] Shandong Univ Technol, Inst Appl Math, Sch Sci, Zibo 255091, Shandong, Peoples R China
关键词
Matrix congruence; Bilinear form; Local ring; Principal ideal ring; FORMS;
D O I
10.1016/j.laa.2009.06.003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let R be a commutative, local, and principal ideal ring with maximal ideal in and residue class field F. Suppose that every element of 1 + m is square. Then the problem of classifying arbitrary symmetric matrices over R by congruence naturally reduces, and is actually equivalent to, the problem of classifying invertible symmetric matrices over F by congruence. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:1687 / 1690
页数:4
相关论文
共 6 条
[1]  
Baeza R, 1978, LECT NOTES MATH, V655
[2]   The Steinberg lattice of a finite Chevalley group and its modular reduction [J].
Gow, R .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 67 :593-608
[3]   CONTRA-VARIANT FORMS ON INDUCED REPRESENTATIONS OF SEMI-SIMPLE LIE-ALGEBRAS [J].
JANTZEN, JC .
MATHEMATISCHE ANNALEN, 1977, 226 (01) :53-65
[4]   Quadratic forms of projective spaces over rings [J].
Levchuk, V. M. ;
Starikova, O. A. .
SBORNIK MATHEMATICS, 2006, 197 (5-6) :887-899
[6]  
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