Geodesic
Polynomial orbits in finite commutative rings
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 711-719 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $R$ be a finite commutative ring with unity. We determine the set of all possible cycle lengths in the ring of polynomials with rational integral coefficients.
Let $R$ be a finite commutative ring with unity. We determine the set of all possible cycle lengths in the ring of polynomials with rational integral coefficients.
Classification : 11C08, 13M05, 13M10
Keywords: polynomial cycles; finite rings 
@article{CMJ_2006_56_2_a33,
     author = {Kone\v{c}n\'a, Petra},
     title = {Polynomial orbits in finite commutative rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {711--719},
     year = {2006},
     volume = {56},
     number = {2},
     mrnumber = {2291769},
     zbl = {1164.11314},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a33/}
}
TY  - JOUR
AU  - Konečná, Petra
TI  - Polynomial orbits in finite commutative rings
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 711
EP  - 719
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a33/
LA  - en
ID  - CMJ_2006_56_2_a33
ER  - 
%0 Journal Article
%A Konečná, Petra
%T Polynomial orbits in finite commutative rings
%J Czechoslovak Mathematical Journal
%D 2006
%P 711-719
%V 56
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a33/
%G en
%F CMJ_2006_56_2_a33
Konečná, Petra. Polynomial orbits in finite commutative rings. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 711-719. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a33/

[1] P. J. Davis: Circulant Matrices. J. Wiley and Sons, NewYork-Chichester-Brisbane-Toronto, 1979. | MR | Zbl

[2] B. R.  McDonald: Finite Rings with Identity. M.  Dekker, New York, 1974. | MR | Zbl

[3] V.  Dubovský: Polynomial cycles. Master Thesis, Department of Mathematics, Faculty of Science, University of Ostrava, 2003. (Czech)

[4] F.  Halter-Koch and P.  Konečná: Polynomial cycles in finite extension fields. Mathematica Slovaca 52 (2002), 531–535. | MR

[5] P.  Konečná: Polynomial orbits in direct sum of finite extension fields. Studia Universitatis “Babes-Bolyai” Mathematica, Vol.  XLVIII, June 2003, pp. 73–77. | MR

[6] W. Narkiewicz: Polynomial Mappings. Lecture Notes in Mathematics Vol.  1600. Springer-Verlag, Berlin, 1995. | MR