The radical factors of f(x)−f(y) over finite fields
Let F denote the finite field of order q For f(x) in F[x], let f*(x,y) denote the substitution polynomial f(x)−f(y). The polynomial f*(x,y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x,y) that are solvable by radicals We sh...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297001087 |
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| author | Javier Gomez-Calderon |
| author_facet | Javier Gomez-Calderon |
| author_sort | Javier Gomez-Calderon |
| collection | DOAJ |
| description | Let F denote the finite field of order q For f(x) in F[x], let f*(x,y) denote the substitution polynomial f(x)−f(y). The polynomial f*(x,y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x,y) that are solvable by
radicals We show that if R(x,y) denotes the product of all the irreducible factors of f*(x,y) that are
solvable by radicals, then R(x,y)=g(x)−g(y) and f(x)=G(g(x)) for some polynomials g(x) and G(x) in F[x]. |
| format | Article |
| id | doaj-art-87706ebcfe874ae589ada4a232e300c8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-87706ebcfe874ae589ada4a232e300c82025-02-03T01:21:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120479980210.1155/S0161171297001087The radical factors of f(x)−f(y) over finite fieldsJavier Gomez-Calderon0Department of Mathematics, New Kensington Campus, The Pennsylvania State University, New Kensington 15068, PA, USALet F denote the finite field of order q For f(x) in F[x], let f*(x,y) denote the substitution polynomial f(x)−f(y). The polynomial f*(x,y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x,y) that are solvable by radicals We show that if R(x,y) denotes the product of all the irreducible factors of f*(x,y) that are solvable by radicals, then R(x,y)=g(x)−g(y) and f(x)=G(g(x)) for some polynomials g(x) and G(x) in F[x].http://dx.doi.org/10.1155/S0161171297001087finite fieldspolynomials. |
| spellingShingle | Javier Gomez-Calderon The radical factors of f(x)−f(y) over finite fields International Journal of Mathematics and Mathematical Sciences finite fields polynomials. |
| title | The radical factors of f(x)−f(y) over finite fields |
| title_full | The radical factors of f(x)−f(y) over finite fields |
| title_fullStr | The radical factors of f(x)−f(y) over finite fields |
| title_full_unstemmed | The radical factors of f(x)−f(y) over finite fields |
| title_short | The radical factors of f(x)−f(y) over finite fields |
| title_sort | radical factors of f x f y over finite fields |
| topic | finite fields polynomials. |
| url | http://dx.doi.org/10.1155/S0161171297001087 |
| work_keys_str_mv | AT javiergomezcalderon theradicalfactorsoffxfyoverfinitefields AT javiergomezcalderon radicalfactorsoffxfyoverfinitefields |