International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 90738, 6 pages
Generalized affine transformation monoids on Galois rings
Institute of Applied Mathematics, School of Mathematics and Information, Shandong University of Technology, Zibo 255091, Shandong, China
Received 10 November 2005; Revised 14 July 2006; Accepted 18 July 2006
Copyright © 2006 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.
Let be a ring with identity. The generalized affine transformation
monoid is defined as the set of all
transformations on of the form
(for all ), where . We study the algebraic
structure of the monoid on a finite Galois ring . The following results are obtained: an explicit description
of Green's relations on ; and an explicit description of the Schützenberger group of every -class, which is shown to be isomorphic to the affine
transformation group for a smaller Galois ring.