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Analytically irreducible polynomials with coefficients in a real-valued field
Author(s):
A.
Granja;
M.
C.
Martínez;
C.
Rodríguez
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3449-3454.
MSC (2010):
Primary 13B25, 12E05;
Secondary 13A05, 13F30
Posted:
April 13, 2010
MathSciNet review:
2661545
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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:
-
- [A]
- S.S. Abhyankar, Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math., 74, no. 2 (1989), 190-257. MR 997097 (90h:32018)
- [E]
- O. Endler, Valuation Theory. Springer-Verlag, Berlin, 1972. MR 0357379 (50:9847)
- [G]
- A. Granja, Irreducible polynomials with coefficients in a complete discrete valuation field. Adv. Math., 109, no. 1 (1994), 75-87. MR 1302757 (95j:13006)
- [HOS]
- F. J. Herrera Govantes, M. A. Olalla Acosta and M. Spivakovsky, Valuations in algebraic field extensions. J. Algebra, 312 (2007), 1033-1074. MR 2333199 (2008e:12007)
- [L]
- S. Lang, Algebra (Revised Third Edition). Graduate Text in Mathematics, 211, Springer-Verlag, New York, 2002. MR 1878556 (2003e:00003)
- [R]
- P. Ribenboim, The Theory of Classical Valuations. Springer-Verlag, New York, 1999. MR 1677964 (2000d:12007)
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- O. Zariski and P. Samuel, Commutative Algebra. Vols. I and II. Reprint of the 1958-60 edition, Graduate Texts in Math., 28-29, Springer-Verlag, New York, 1979. MR 0384768 (52:5641), MR 0389876 (52:10706)
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Additional Information:
A.
Granja
Affiliation:
Departamento de Matemáticas, Universidad de León, 24071-León, Spain
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
DOI:
10.1090/S0002-9939-10-10357-8
PII:
S 0002-9939(10)10357-8
Received by editor(s):
September 28, 2009
Received by editor(s) in revised form:
December 30, 2009
Posted:
April 13, 2010
Additional Notes:
This work was partially supported by MCI, MTM2009-11433 and JCYL, LE003A09.
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
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