Week graded analogues of Gauss lemma and Eisenstein criterion
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 813-816
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.
@article{FPM_1995_1_3_a17,
author = {A. N. Khaikin},
title = {Week graded analogues of {Gauss} lemma and {Eisenstein} criterion},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {813--816},
year = {1995},
volume = {1},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a17/}
}
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/
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[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