Abstract
We describe a method for constructing classes of bivariate polynomials which are irreducible over algebraically closed fields of characteristic zero. The constructions make use of some factorization conditions and apply to classes of polynomials that includes the generalized difference polynomials.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Angermüller, G.: A generalization of Ehrenfeucht’s irreducibility criterion. J. Number Theory 36, 80–84 (1990)
Ayad, M.: Sur les polynômes f(X,Y) tels que K[f] est intégralement fermé dans K[X,Y]. Acta Arith. 105, 9–28 (2002)
Bhatia, S., Khanduja, S.K.: Difference polynomials and their generalizations. Mathematika 48, 293–299 (2001)
Bishnoi, A., Khanduja, S.K., Sudesh, K.: Some extensions and applications of the Eisenstein irreducibility criterion. Developments in Mathematics 18, 189–197 (2010)
Cohen, S.D., Movahhedi, A., Salinier, A.: Factorization over local fields and the irreducibility of generalized difference polynomials. Mathematika 47, 173–196 (2000)
Panaitopol, L., Ştefănescu, D.: On the generalized difference polynomials. Pacific J. Math. 143, 341–348 (1990)
Rubel, L.A., Schinzel, A., Tverberg, H.: On difference polynomials and hereditary irreducible polynomials. J. Number Theory 12, 230–235 (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Ştefănescu, D. (2013). Construction of Classes of Irreducible Bivariate Polynomials. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-319-02297-0_32
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02296-3
Online ISBN: 978-3-319-02297-0
eBook Packages: Computer ScienceComputer Science (R0)