Generalized affine transformation monoids on Galois rings
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↦xu+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:...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/90738 |
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| Summary: | 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↦xu+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. |
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| ISSN: | 0161-1712 1687-0425 |