Geodesic
The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 64-84

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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},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a4/}
}
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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/