Geodesic
A generalization of Ore's theorem on irreducible polynomials over a finite field
Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 108-110.

Voir la notice de l'article provenant de la source Math-Net.Ru

For an arbitrary prime power $q$, a criterion for irreducibility of a polynomial of the form $$ F(x) = x^{q^{m}-1}+a_{m-1}x^{q^{m-1}-1}+\ldots+a_1x^{q-1}+a_0, \ a_0\neq 0, $$ over the field $K = GF(q^t)$ is established.
Keywords: irreducible polynomials, irreducibility criterion. 
@article{DM_2015_27_1_a7,
     author = {A. A. Nechaev and V. O. Popov},
     title = {A generalization of {Ore's} theorem on irreducible polynomials over a finite field},
     journal = {Diskretnaya Matematika},
     pages = {108--110},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/}
}
TY  - JOUR
AU  - A. A. Nechaev
AU  - V. O. Popov
TI  - A generalization of Ore's theorem on irreducible polynomials over a finite field
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 108
EP  - 110
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/
LA  - ru
ID  - DM_2015_27_1_a7
ER  - 
%0 Journal Article
%A A. A. Nechaev
%A V. O. Popov
%T A generalization of Ore's theorem on irreducible polynomials over a finite field
%J Diskretnaya Matematika
%D 2015
%P 108-110
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/
%G ru
%F DM_2015_27_1_a7
A. A. Nechaev; V. O. Popov. A generalization of Ore's theorem on irreducible polynomials over a finite field. Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 108-110. http://geodesic.mathdoc.fr/item/DM_2015_27_1_a7/

[1] Dzhekobson N., Teoriya kolets, GIIL, M., 1947, 266 pp.

[2] Ore O., “Contribution to the theory of finite fields”, Trans. Amer. Math. Soc., 37:2 (1973), 241–242

[3] McDonald B. R., Finite Rings with Identity, Markel Dekker, New York, 1974 | MR | Zbl

[4] Popov V. O., “Kriterii neprivodimosti mnogochlenov spetsialnogo vida nad konechnym neprostym polem”, 5 Vsesoyuznyi simpozium po teorii kolets, algebr i modulei, Tezisy soobschenii, Novosibirsk, 1982, 104–105