ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS

被引:3
作者
Khanduja, Sudesh K. [1 ]
Kumar, Sanjeev [2 ]
机构
[1] Indian Inst Sci Educ & Res IISER Mohali, Sas Nagar 140306, Punjab, India
[2] Panjab Univ, Dept Math, Chandigarh 160014, India
关键词
Valued fields; non-Archimedean valued fields; irreducible polynomials; EXTENSIONS; THEOREM;
D O I
10.1142/S0219498812501253
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 Schonemann 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.
引用
收藏
页数:10
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