A generalization of Eisenstein–Schönemann irreducibility criterion
A generalization of Eisenstein–Schönemann irreducibility criterion
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Eisenstein-Schönemann 不可约性准则的推广
DOI：
10.1007/s00229-010-0393-x
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发表时间：
2011
影响因子：
0.6
通讯作者：
Ramneek Khassa
中科院分区：
文献类型：
--
作者：
S. K. Khanduja;Ramneek Khassa
推广了Eisenstein不可约性判据的一个结果说，如果是一个多项式，其系数来自整数环，使得对某些人来说，每个不可除旁路都不能被素数整除，并且0不能除以旁路2，则至少在有理数域上有一个不可约次数因子。我们已经观察到，如果如上所述，则它在p-进整数环上有一个次数为g(X)的不可约因子，使得g(X)是关于top的Eisenstein多项式。在这篇文章中，我们证明了一类更广泛的多项式的上述结果的类似结果，它将推广经典的Schönemann不可约性判据和广义Schönemann不可约性判据，并得到Akira等人的不可约性判据。(J数论25：107-111,1987)。
One of the results generalizing Eisenstein Irreducibility Criterion states that ifis a polynomial with coefficients from the ring of integers such thatasis not divisible by a primepfor some, eachaiis divisible bypforanda0is not divisible byp2, thenhas an irreducible factor of degree at leastsover the field of rational numbers. We have observed that ifis as above, then it has an irreducible factorg(x) of degreesover the ring ofp-adic integers such thatg(x) is an Eisenstein polynomial with respect top. 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).