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Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 2, Pages 47–60 (Mi faa39)  

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

Koszul Algebras and Their Ideals

D. I. Piontkovskii

Central Economics and Mathematics Institute, RAS

Abstract: We study associative graded algebras that have a “complete flag” of cyclic modules with linear free resolutions, i.e., algebras over which there exist cyclic Koszul modules with any possible number of relations (from zero to the number of generators of the algebra). Commutative algebras with this property were studied in several papers by Conca and others. Here we present a noncommutative version of their construction.
We introduce and study the notion of Koszul filtration in a noncommutative algebra and examine its connections with Koszul algebras and algebras with quadratic Gröbner bases. We consider several examples, including monomial algebras, initially Koszul algebras, generic algebras, and algebras with one quadratic relation. It is shown that every algebra with a Koszul filtration has a rational Hilbert series.

Keywords: Koszul filtration, coherent algebra, Koszul algebra, Hilbert series

DOI: https://doi.org/10.4213/faa39

Full text: PDF file (237 kB)
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English version:
Functional Analysis and Its Applications, 2005, 39:2, 120–130

Bibliographic databases:

UDC: 512.66
Received: 21.05.2003

Citation: D. I. Piontkovskii, “Koszul Algebras and Their Ideals”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 47–60; Funct. Anal. Appl., 39:2 (2005), 120–130

Citation in format AMSBIB
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\paper Koszul Algebras and Their Ideals
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\yr 2005
\vol 39
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\pages 47--60
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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. D. I. Piontkovskii, “Sets of Hilbert series and their applications”, J. Math. Sci., 139:4 (2006), 6753–6761  mathnet  crossref  mathscinet  zmath
    2. Piontkovski D., “Linear equations over noncommutative graded rings”, J. Algebra, 294:2 (2005), 346–372  crossref  mathscinet  zmath  isi  elib  scopus
    3. Piontkovski D., Silvestrov S.D., “Cohomology of 3-dimensional color Lie algebras”, J. Algebra, 316:2 (2007), 499–513  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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