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Generalized affine transformation monoids on Galois rings

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  • Yonglin Cao

Abstract

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 x ↦ x u + a (for all x ∈ A ), where u , a ∈ A . 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 -class, which is shown to be isomorphic to the affine transformation group for a smaller Galois ring.

Suggested Citation

  • Yonglin Cao, 2006. "Generalized affine transformation monoids on Galois rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-6, September.
    • Handle: RePEc:hin:jijmms:090738
    DOI: 10.1155/IJMMS/2006/90738
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