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Sib. Èlektron. Mat. Izv., 2007, Volume 4, Pages 64–84 (Mi semr145)  

This article is cited in 3 scientific papers (total in 3 papers)

Research papers

The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings

E. Yu. Daniyarova

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: 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.

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Bibliographic databases:

Document Type: Article
UDC: 512.55
MSC: 13C99
Received February 14, 2006, published March 15, 2007

Citation: E. Yu. Daniyarova, “The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings”, Sib. Èlektron. Mat. Izv., 4 (2007), 64–84

Citation in format AMSBIB
\Bibitem{Dan07}
\by E.~Yu.~Daniyarova
\paper The $Q$-ideals in polynomial rings and the $Q$-modules over polynomial rings
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 64--84
\mathnet{http://mi.mathnet.ru/semr145}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2465415}
\zmath{https://zbmath.org/?q=an:1132.13300}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Yu. Daniyarova, “Metabelevy $U$-algebry Li”, Sib. elektron. matem. izv., 5 (2008), 355–382  mathnet  mathscinet  elib
    2. E. Yu. Daniyarova, “Metabelevy $Q$-algebry Li”, Sib. elektron. matem. izv., 6 (2009), 26–48  mathnet  mathscinet
    3. E. Yu. Daniyarova, “Aksiomy metabelevykh Q-algebr i U-algebr Li”, Sib. elektron. matem. izv., 9 (2012), 266–284  mathnet
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