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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832555066157957120 |
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| author | Yonglin Cao |
| author_facet | Yonglin Cao |
| author_sort | Yonglin Cao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ad38f42cf94645229e28e1757df7d536 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ad38f42cf94645229e28e1757df7d5362025-02-03T05:49:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/9073890738Generalized affine transformation monoids on Galois ringsYonglin Cao0Institute of Applied Mathematics, School of Mathematics and Information, Shandong University of Technology, Zibo, Shandong 255091, ChinaLet 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.http://dx.doi.org/10.1155/IJMMS/2006/90738 |
| spellingShingle | Yonglin Cao Generalized affine transformation monoids on Galois rings International Journal of Mathematics and Mathematical Sciences |
| title | Generalized affine transformation monoids on Galois rings |
| title_full | Generalized affine transformation monoids on Galois rings |
| title_fullStr | Generalized affine transformation monoids on Galois rings |
| title_full_unstemmed | Generalized affine transformation monoids on Galois rings |
| title_short | Generalized affine transformation monoids on Galois rings |
| title_sort | generalized affine transformation monoids on galois rings |
| url | http://dx.doi.org/10.1155/IJMMS/2006/90738 |
| work_keys_str_mv | AT yonglincao generalizedaffinetransformationmonoidsongaloisrings |