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Matematicheskie Zametki, 2009, Volume 85, Issue 5, Pages 721–736
DOI: https://doi.org/10.4213/mzm6909 (Mi mzm6909) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Monomial Modules and Graded Betti Numbers

M. Crupi, G. Restuccia

University of Messina
Full-text PDF (465 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm6909
Abstract: Let KK be a field, S=K[x1,…,xn]S=K[x1,…,xn], the polynomial ring over KK, and let FF be a finitely generated graded free SS-module with homogeneous basis. Certain invariants, such as the Castelnuovo–Mumford regularity and the graded Betti numbers of submodules of FF, are studied; in particular, the componentwise linear submodules of FF are characterized in terms of their graded Betti numbers.
Keywords: graded ring, graded module, minimal graded free resolution, graded Betti number, polynomial ring, Gröbner basis, syzygy module.
Received: 18.01.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 5, Pages 690–702
DOI: https://doi.org/10.1134/S0001434609050095
Bibliographic databases:
UDC: 512.626
Language: Russian
Citation: M. Crupi, G. Restuccia, “Monomial Modules and Graded Betti Numbers”, Mat. Zametki, 85:5 (2009), 721–736; Math. Notes, 85:5 (2009), 690–702
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    1. Failla G., Stagliano P.L., “S-Sequences and Monomial Modules”, Mathematics, 9:21 (2021), 2659  crossref  isi
    2. Amata L., Crupi M., “A Generalization of Kruskal-Katona'S Theorem”, Analele Stiint. Univ. Ovidius C., 28:2 (2020), 35–51  crossref  mathscinet  isi
    3. Amata L., Crupi M., “Minimal Resolutions of Graded Modules Over An Exterior Algebra”, Atti Accad. Pelorit. Pericol., 97:1 (2019), A5  crossref  mathscinet  isi
    4. Crupi M., “Extremal Betti Numbers of Graded Modules”, J. Pure Appl. Algebr., 220:6 (2016), 2277–2288  crossref  mathscinet  zmath  isi  scopus
    5. Crupi M., Ferro C., “Squarefree Monomial Modules and Extremal Betti Numbers”, Algebr. Colloq., 23:3 (2016), 519–530  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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