Geodesic
Week graded analogues of Gauss lemma and Eisenstein criterion
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 813-816.

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This paper continues a series of investigations, devoted to generalized forms of Gauss lemma and Eisenstein criterion. Thus in papers [1] and [2] statements for rings with derivations are given, and in [3] those for $Z$- and $Z^+$-graded rings. In this paper $Z^+$-weak graded rings (which include two previous classes) are considered. Theorem 1 is an analog of Eisenstein criterion, theorem 2 is an analog of Gauss lemma. Some improvement of the result of Kovachich [1] follows from these theorems. Partial necessity of some sufficient conditions introduced in the paper has been demonstrated in theorem 3. 
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A. N. Khaikin. Week graded analogues of Gauss lemma and Eisenstein criterion. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 813-816. http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a17/

[1] Kovačič J., “Eisenstein criterion for noncommutative polynomials”, Proc. Amer. Math. Soc., 34, no. 1, 1972, 25–29 | MR | Zbl

[2] Berkovich L. M., “Analog kriteriya Eizenshteina dlya obyknovennykh lineinykh differentsialnykh uravnenii”, Mezhvuzovskii sbornik nauchnykh statei, Kuibyshev, 1988, 20–27 | MR | Zbl

[3] Bavula V. V., “O nekotorykh obobscheniyakh kriteriya Eizenshteina”, Ukr. mat. zhurn., 42:7, 983–985 | MR | Zbl