Geodesic
The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 64-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we introduce the new categories of ideals in commutative rings of polynomials and of modules over rings of polynomials. This material proposes the definitions of linear ideal, $Q$ ideal of ring of commutative polynomials over a field, $Q$ radical, linear homomorphism between rings of polynomials and investigates the features of such objects. We cast the definition of $Q$ module over a ring of polynomials and examine the structure of such modules. In particular, it is developed the theory of primary decomposition of $Q$ modules. Also we prove that arbitrary $Q$ module can be decomposed in direct sum of torsion-free modules. 
@article{SEMR_2007_4_a4,
     author = {E. Yu. Daniyarova},
     title = {The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {64--84},
     year = {2007},
     volume = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a4/}
}
TY  - JOUR
AU  - E. Yu. Daniyarova
TI  - The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2007
SP  - 64
EP  - 84
VL  - 4
UR  - http://geodesic.mathdoc.fr/item/SEMR_2007_4_a4/
LA  - ru
ID  - SEMR_2007_4_a4
ER  - 
%0 Journal Article
%A E. Yu. Daniyarova
%T The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2007
%P 64-84
%V 4
%U http://geodesic.mathdoc.fr/item/SEMR_2007_4_a4/
%G ru
%F SEMR_2007_4_a4
E. Yu. Daniyarova. The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 64-84. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a4/

[1] E. Yu. Daniyarova, Osnovy algebraicheskoi geometrii nad algebrami Li, Preprint No 131, RAN Sib. Otd-nie, In-t matematiki, Novosibirsk, 2004, 33 pp.

[2] E. Yu. Daniyarova, I. V. Kazachkov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li I: $U$ algebry i universalnye klassy”, Fundam. i prikl. mat., 9:3 (2003), 37–63 http://mech.math.msu.su/textasciitilde fpm/rus/k03/k033/k03304h.htm | MR | Zbl

[3] E. Yu. Daniyarova, I. V. Kazachkov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li II: Sluchai konechnogo polya”, Fundam. i prikl. mat., 9:3 (2003), 65–87 http://mech.math.msu.su/textasciitilde fpm/rus/k03/k033/k03305h.htm | MR | Zbl

[4] E. Yu. Daniyarova, Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li III: $Q$ algebry i koordinatnye algebry algebraicheskikh mnozhestv, Preprint, Izd-vo OmGU, Omsk, 2005, 130 pp.

[5] E. Yu. Daniyarova, I. V. Kazachkov, V. N. Remeslennikov, Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li I: $U$ algebry i $A$ moduli, Preprint No 34, OmGAU, Omsk, 2001, 25 pp.

[6] S. Leng, Algebra, Mir, Moskva, 1968

[7] N. Burbaki, Kommutativnaya algebra, Mir, Moskva, 1971