On a generalization of Eisenstein's irreducibility criterion

Khanduja, Sudesh K. ; Saha, Jayanti (1997) On a generalization of Eisenstein's irreducibility criterion Mathematika, 44 (1). pp. 37-41. ISSN 0025-5793

Full text not available from this repository.

Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S0025579300011931


Let ν be a valuation of any rank of a field K with value group Gν and f(X)= Xm + alXm−1 + … + am be a polynomial over K. In this paper, it is shown that if (ν(ai)/i)≥(ν(am)/m)>0 for l≤i≤m, and there does not exist any integer r>1 dividing m such that ν(am)/r∈Gν, then f(X) is irreducible over K. It is derived as a special case of a more general result proved here. It generalizes the usual Eisenstein Irreducibility Criterion and an Irreducibility Criterion due to Popescu and Zaharescu for discrete, rank-1 valued fields, (cf. [Journal of Number Theory, 52 (1995), 98–118]).

Item Type:Article
Source:Copyright of this article belongs to University College London.
Keywords:12E05; Field Theory and Polynomials; General Field Theory; Polynomials (Irreducibility).
ID Code:69877
Deposited On:19 Nov 2011 10:23
Last Modified:19 Nov 2011 10:23

Repository Staff Only: item control page