ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS
2012 ◽
Vol 12
(01)
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pp. 1250125
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Keyword(s):
Let (K, v) be a complete rank-1 valued field. In this paper, we extend classical Hensel's Lemma to residually transcendental prolongations of v to a simple transcendental extension K(x) and apply it to prove a generalization of Dedekind's theorem regarding splitting of primes in algebraic number fields. We also deduce an irreducibility criterion for polynomials over rank-1 valued fields which extends already known generalizations of Schönemann Irreducibility Criterion for such fields. A refinement of Generalized Akira criterion proved in Khanduja and Khassa [Manuscripta Math.134(1–2) (2010) 215–224] is also obtained as a corollary of the main result.
1999 ◽
Vol 42
(3)
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pp. 469-480
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Keyword(s):
1991 ◽
Vol 1991
(416)
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pp. 187-194
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Keyword(s):
2012 ◽
Vol 27
(22)
◽
pp. 1250112