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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 2, Pages 47–60
DOI: https://doi.org/10.4213/faa39 (Mi faa39) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Koszul Algebras and Their Ideals

D. I. Piontkovskii

Central Economics and Mathematics Institute, RAS
Full-text PDF (237 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa39
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.
Received: 21.05.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 2, Pages 120–130
DOI: https://doi.org/10.1007/s10688-005-0024-6
Bibliographic databases:
Document Type: Article
UDC: 512.66
Language: Russian
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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  • https://doi.org/10.4213/faa39
  • https://www.mathnet.ru/eng/faa/v39/i2/p47
    • This publication is cited in the following 6 articles:
    1. Cassella A., Quadrelli C., “Right-Angled Artin Groups and Enhanced Koszul Properties”, J. Group Theory, 24:1 (2021), 17–38  crossref  mathscinet  isi
    2. Quadrelli C., “Pro-P Groups With Few Relations and Universal Koszulity”, Math. Scand., 127:1 (2021), 28–42  crossref  mathscinet  isi
    3. Minac J. Palaisti M. Pasini F.W. Nguyen Duy Tan, “Enhanced Koszul Properties in Galois Cohomology”, Res. Math. Sci., 7:2 (2020), 10  crossref  mathscinet  isi
    4. 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
    5. Piontkovski D., “Linear equations over noncommutative graded rings”, J. Algebra, 294:2 (2005), 346–372  crossref  mathscinet  zmath  isi  elib  scopus
    6. D. I. Piontkovskii, “Sets of Hilbert series and their applications”, J. Math. Sci., 139:4 (2006), 6753–6761  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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