Algebraicity in local rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 5, pp. 161-170.

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

In this paper, we study skew polynomials over local rings, their roots and decompositions. We introduce the concept of an algebraic set in a local ring and study this concept using the theory of skew polynomials.
@article{FPM_2007_13_5_a5,
     author = {I. O. Kachkovskii},
     title = {Algebraicity in local rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {161--170},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_5_a5/}
}
TY  - JOUR
AU  - I. O. Kachkovskii
TI  - Algebraicity in local rings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2007
SP  - 161
EP  - 170
VL  - 13
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2007_13_5_a5/
LA  - ru
ID  - FPM_2007_13_5_a5
ER  - 
%0 Journal Article
%A I. O. Kachkovskii
%T Algebraicity in local rings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2007
%P 161-170
%V 13
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2007_13_5_a5/
%G ru
%F FPM_2007_13_5_a5
I. O. Kachkovskii. Algebraicity in local rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 5, pp. 161-170. http://geodesic.mathdoc.fr/item/FPM_2007_13_5_a5/

[1] Barantsev A. V., “Kosye mnogochleny nad lokalnymi koltsami”, Fundament. i prikl. mat., 2:4 (1996), 1155–1162 | MR | Zbl

[2] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[3] Lambek I., Koltsa i moduli, Mir, M., 1971 | MR | Zbl

[4] Kherstein I., Nekommutativnye koltsa, Mir, M., 1972 | MR

[5] Gelfand I., Retakh V., Wilson R. L., “Quadratic linear algebras associated with factorizations of noncommutative polynomials and noncommutative differential polynomials”, Selecta Math. (N.S.), 7 (2001), 493–523 | DOI | MR | Zbl

[6] Lam T. Y., A First Course in Noncommutative Rings, Springer, Berlin, 1991 | MR

[7] Lam T. Y., “A general theory of Vandermonde matrices”, Exposition. Math., 4 (1986), 193–215 | MR | Zbl

[8] Lam T. Y., Leroy A., “Vandermonde and Wronskian matrices over division rings”, J. Algebra, 119 (1988), 308–336 | DOI | MR | Zbl

[9] Lam T. Y., Leroy A., “Hilbert 90 theorems over division rings”, Trans. Amer. Math. Soc., 345:2 (1994), 595–622 | DOI | MR | Zbl