International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 90738, 6 pages

Generalized affine transformation monoids on Galois rings

Yonglin Cao

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 A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form xxu+a (for all xA), where u,aA. We study the algebraic structure of the monoid Gaff(A) on a finite Galois ring A. The following results are obtained: an explicit description of Green's relations on Gaff(A); and an explicit description of the Schützenberger group of every 𝒟-class, which is shown to be isomorphic to the affine transformation group for a smaller Galois ring.