Analytically irreducible polynomials with coefficients in a real-valued field
HTML articles powered by AMS MathViewer
- by A. Granja, M. C. Martínez and C. Rodríguez PDF
- Proc. Amer. Math. Soc. 138 (2010), 3449-3454 Request permission
Abstract:
In this paper, we show a criterion of analytic irreducibility for polynomials with coefficients in a real-valued field. This generalizes previous criteria of Abhyankar as well as those of Granja.References
- Shreeram S. Abhyankar, Irreducibility criterion for germs of analytic functions of two complex variables, Adv. Math. 74 (1989), no. 2, 190–257. MR 997097, DOI 10.1016/0001-8708(89)90009-1
- Otto Endler, Valuation theory, Universitext, Springer-Verlag, New York-Heidelberg, 1972. To the memory of Wolfgang Krull (26 August 1899–12 April 1971). MR 0357379, DOI 10.1007/978-3-642-65505-0
- Angel Granja, Irreducible polynomials with coefficients in a complete discrete valuation field, Adv. Math. 109 (1994), no. 1, 75–87. MR 1302757, DOI 10.1006/aima.1994.1080
- F. J. Herrera Govantes, M. A. Olalla Acosta, and M. Spivakovsky, Valuations in algebraic field extensions, J. Algebra 312 (2007), no. 2, 1033–1074. MR 2333199, DOI 10.1016/j.jalgebra.2007.02.022
- Serge Lang, Algebra, 3rd ed., Graduate Texts in Mathematics, vol. 211, Springer-Verlag, New York, 2002. MR 1878556, DOI 10.1007/978-1-4613-0041-0
- Paulo Ribenboim, The theory of classical valuations, Springer Monographs in Mathematics, Springer-Verlag, New York, 1999. MR 1677964, DOI 10.1007/978-1-4612-0551-7
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. 1, Graduate Texts in Mathematics, No. 28, Springer-Verlag, New York-Heidelberg-Berlin, 1975. With the cooperation of I. S. Cohen; Corrected reprinting of the 1958 edition. MR 0384768
Additional Information
- A. Granja
- Affiliation: Departamento de Matemáticas, Universidad de León, 24071-León, Spain
- MR Author ID: 76125
- ORCID: 0000-0002-7487-892X
- Email: angel.granja@unileon.es
- M. C. Martínez
- Affiliation: Departamento de Matemática Aplicada, Universidad de Valladolid, 47014-Valladolid, Spain
- Email: carmen@mat.uva.es
- C. Rodríguez
- Affiliation: Departamento de Matemáticas, Universidad de León, 24071-León, Spain
- Email: mcrods@unileon.es
- Received by editor(s): September 28, 2009
- Received by editor(s) in revised form: December 30, 2009
- Published electronically: April 13, 2010
- Additional Notes: This work was partially supported by MCI, MTM2009-11433 and JCYL, LE003A09.
- Communicated by: Bernd Ulrich
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 3449-3454
- MSC (2010): Primary 13B25, 12E05; Secondary 13A05, 13F30
- DOI: https://doi.org/10.1090/S0002-9939-10-10357-8
- MathSciNet review: 2661545