PERMUTATION POLYNOMIALS IN ONE INDETERMINATE OVER MODULAR ALGEBRAS

Pablo A. Acosta-Solarte; Víctor S. Albis

doi:10.18257/raccefyn.30(117).2006.2281

Vol. 30 No. 117 (2006), Mathematics

Vol. 30 No. 117 (2006)

PERMUTATION POLYNOMIALS IN ONE INDETERMINATE OVER MODULAR ALGEBRAS

Mathematics

https://doi.org/10.18257/raccefyn.30(117).2006.2281

Published 2023-11-25

Pablo A. Acosta-Solarte⁺⁻
Víctor S. Albis⁺⁻

Pablo A. Acosta-Solarte

Universidad Distrital Francisco José de Caldas, Bogotá, Colombia.

Víctor S. Albis

Universidad Nacional de Colombia, Bogotá, Colombia.

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How to Cite

Acosta-Solarte, P. A., & Albis, V. S. (2023). PERMUTATION POLYNOMIALS IN ONE INDETERMINATE OVER MODULAR ALGEBRAS. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 30(117), 541–548. https://doi.org/10.18257/raccefyn.30(117).2006.2281

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Pablo A. Acosta-Solarte, Víctor S. Albis, PERMUTATION POLYNOMIALS IN ONE INDETERMINATE OVER MODULAR ALGEBRAS , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 31 No. 120 (2007)
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Abstract

Known results on permutation polynomials with coefficients in a finite field are extended to algebras of the form Lv=K[X]/(p(X)v)), where K is a finite field, p(X) belongs to K[X] and is an irreducible polynomial, v = 1,2..., and to the algebra of power series L[[Z]]. Finally analogues of Dickson polynomials in these algebras are studied.

https://doi.org/10.18257/raccefyn.30(117).2006.2281

Keywords

Permutation polynomial | Dickson polynomial

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References

Albis, V. S. Polinomios de permutation. Algunos problemas de interés, Lecturas Matemáticas 22 (2001), 35-58.

Albis, V. S. & Chaparro, R. On a conjecture of Borevich and Shafarevich, Rev. Acad. Colomb. Cienc. 21 (1997), 313-319. [MR: 98g:11130].

Daqing, W. Permutation binomials over finite fields, Acta Math. Sinica. 10 (1994), 30-35. [MR: 94m:11145].

Dickson, L. E. Linear Groups with an Exposition of the Galois Field Theory. Dover Publi: New York, 1958.

Fried, M. On a conjecture of Schur, Michigan Math. J..17 No. 1 (1970), 41-55. [MR: 41# 1688).

Greenberg, M. J. Lectures on Forms in Many Variables. W. A. Benjamin, New York, 1969.

Lidl, R. & Mullen, G. L When does a polynomial over a finite field permute the elements of the field?, Amer. Math. Month. 95 (1988), 243-246.

Lidl, R. & Niederreiter, H. Finite Fields, Encycl. of Math and its Appl., Addison Wesley Pub. Comp. Reading Mass., 1983. [MR: 86c: 11106].

McDonald, B. R. Finite Rings with Identity, Marcel Dekker, New York, 1974.

Smits, T. H. On the group of units of GF(q)[X]/(a(X)). Indag. Math. 44 (1982), 355-358.

Sun, Q. A note on permutation polynomials vectors over Z/mZ, Adv. Math. (China) 25 No. 1 (1996), 311-314. [In Chinese] [MR: 98h:11157].

Zhang, Q. On the polynomials in several indeterminates which on be extended to permutation polynomial vector over Z/p/Z, Adv. Math. 22 No. 3 (1993), 456-457.

Zhang, Q. Permutation polynomials in several indeterminates over Z/mZ, Chinese Ann, Math. Ser. A. 16 No. 2 (1995), 168-172. [In Chinese] [MR: 96g: 11143].