abstract
(3 × 3) matrices are here classified up to the relation of projective congruence. This is then applied to obtain the classification up to isomorphism of a certain class of finite rings of characteristic p. These rings arise naturally in the recent determination of all rings of order p n (n ≤ 5) by B. Corbas and the author, and the work here completes that study.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Corbas and G. D. Williams, Rings of order p5, Part I: Nonlocal rings. J.Algebra 231, 677–690 (2000).
B. Corbas and G. D. Williams, Rings of order p5, Part II: Local rings. J.Algebra 231, 691–704 (2000).
B. Corbas and G. D. Williams, Congruence of two-dimensional subspaces in M2(K) (characteristic ≠ 2). Pacific J. Math. 188, 225–235 (1999).
B. Corbas and G. D. Williams, Congruence of two-dimensional subspaces in M2(K) (characteristic 2). Pacific J. Math. 188, 237–249 (1999).
B. Corbas and G. D. Williams, Congruence classes in M3(Fq) (q odd). Discrete Math. 219, 37–47 (2000).
B. Corbas and G. D. Williams, Matrix representatives for three-dimensional bilinear forms over finite fields. Discrete Math. 185, 51–61 (1998).
N. Jacobson, Basic Algebra I. Freeman, San Francisco 1974.
G. D. Williams, On a class of finite rings of characteristic p2. Result. Math. 38, 377–390 (2000).
G. D. Williams, Congruence of (2 × 2) matrices. Discrete Math. 224, 293–297 (2000).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Williams, G.D. Projective Congruence in M3(Fq . Results. Math. 41, 396–402 (2002). https://doi.org/10.1007/BF03322782
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322782