A generalization of Eisenstein-Schönemann irreducibility criterion

Khanduja, Sudesh K. ; Khassa, Ramneek (2011) A generalization of Eisenstein-Schönemann irreducibility criterion Manuscripta Mathematica, 134 (1-2). pp. 215-224. ISSN 0025-2611

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Official URL: http://www.springerlink.com/content/3r282713453280...

Related URL: http://dx.doi.org/10.1007/s00229-010-0393-x


One of the results generalizing Eisenstein Irreducibility Criterion states that if φ(x) = anxn+ an-1xn-1 +...+ a0 is a polynomial with coefficients from the ring of integers such that a s is not divisible by a prime p for some , each a i is divisible by p for and a 0 is not divisible by p2 , then φ(x) has an irreducible factor of degree at least s over the field of rational numbers. We have observed that if φ(x) is as above, then it has an irreducible factor g(x) of degree s over the ring of p-adic integers such that g(x) is an Eisenstein polynomial with respect to p. In this paper, we prove an analogue of the above result for a wider class of polynomials which will extend the classical Schönemann Irreducibility Criterion as well as Generalized Schönemann Irreducibility Criterion and yields irreducibility criteria by Akira et al. (J Number Theory 25:107–111, 1987).

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Deposited On:19 Nov 2011 11:16
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