Pournaki, M. R.; Poursoltani, M.; Terai, N.; Yassemi, S. On the dimension of dual modules of local cohomology and the Serre’s condition for the unmixed Stanley-Reisner ideals of small height. (English) Zbl 1522.13035 J. Algebra 632, 751-782 (2023). Reviewer: Luca Amata (Messina) MSC: 13H10 13F55 05E40 05E45 × Cite Format Result Cite Review PDF Full Text: DOI
Eddamane, Elhousseine; Aqalmoun, Mohamed Arithmetical rank for some class of commutative rings. (English) Zbl 07860031 Moroccan J. Algebra Geom. Appl. 1, No. 2, 402-408 (2022). MSC: 13A15 13B02 13B10 × Cite Format Result Cite Review PDF Full Text: Link
Lajmiri, Bahareh; Rahmati, Farhad Properties of \(t\)-spread principal Borel ideals generated in degree two. (English) Zbl 1488.13046 Facta Univ., Ser. Math. Inf. 35, No. 1, 131-140 (2020). MSC: 13D02 13H10 05E40 13C14 × Cite Format Result Cite Review PDF Full Text: DOI
Saremi, Hero; Mafi, Amir Unmixedness and arithmetic properties of matroidal ideals. (English) Zbl 1436.13027 Arch. Math. 114, No. 3, 299-304 (2020). Reviewer: S. A. Seyed Fakhari (Tehran) MSC: 13C40 13F20 13C13 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Barile, Margherita; Macchia, Antonio On determinantal ideals and algebraic dependence. (English) Zbl 1455.13003 Commun. Algebra 47, No. 6, 2357-2366 (2019). MSC: 13A15 14M10 14M12 13D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
García Dupont, Luis Alfredo; Ramírez Mendoza, Daniel Gualtiero; Olivarez Rodríguez, Miriam The arithmetical rank of \(k\)-complete ideals. (English) Zbl 1455.13004 J. Math. Ext. 12, No. 4, 101-113 (2018). MSC: 13A15 05E40 05E45 × Cite Format Result Cite Review PDF Full Text: Link
Barile, Margherita; Macchia, Antonio The arithmetical rank of the edge ideals of cactus graphs. (English) Zbl 1386.13007 Commun. Algebra 45, No. 12, 5407-5419 (2017). Reviewer: Hero Saremi (Sanandaj) MSC: 13A15 13F55 14M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Katsabekis, Anargyros Arithmetical rank of binomial ideals. (English) Zbl 1421.13005 Arch. Math. 109, No. 4, 323-334 (2017). Reviewer: Christos Tatakis (Mitilini) MSC: 13F20 14M12 05C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Kimura, Kyouko; Mantero, Paolo Arithmetical rank of strings and cycles. (English) Zbl 1364.13021 J. Commut. Algebra 9, No. 1, 89-106 (2017). Reviewer: S. A. Seyed Fakhari (Tehran) MSC: 13F55 13A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Barile, Margherita A note on rational normal scrolls. (English) Zbl 1367.13003 J. Commut. Algebra 9, No. 1, 21-29 (2017). Reviewer: Marcel Morales (Saint-Martin-d’Hères) MSC: 13A15 14J26 14M10 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Seyyedi, Seyyede Masoome; Rahmati, Farhad Cohen Macaulayness and arithmetical rank of generalized theta graphs. (English) Zbl 1370.13012 Mathematics 4, No. 3, Paper No. 43, 18 p. (2016). Reviewer: Fahime Khoshahang (Ilam) MSC: 13C14 13D05 16E10 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Barile, Margherita; Macchia, Antonio The arithmetical rank of the edge ideals of graphs with pairwise disjoint cycles. (English) Zbl 1350.13004 J. Algebra Appl. 15, No. 7, Article ID 1650120, 22 p. (2016). Reviewer: S. A. Seyed Fakhari (Tehran) MSC: 13A15 13F55 05C38 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita; Macchia, Antonio A note on Cohen-Macaulay graphs. (English) Zbl 1361.05062 Commun. Algebra 44, No. 4, 1473-1477 (2016). Reviewer: T. Tamizh Chelvam (Tamilnadu) MSC: 05C25 13A15 13F55 × Cite Format Result Cite Review PDF Full Text: DOI
Gui, Dehuai; Li, Rong Arithmetical rank of the edge ideals of some \(n^-\) cyclic graphs with a common vertex. (Chinese. English summary) Zbl 1349.05209 J. Anhui Norm. Univ., Nat. Sci. 38, No. 6, 524-527 (2015). MSC: 05C50 15A03 13C10 13C15 × Cite Format Result Cite Review PDF Full Text: DOI
Pournaki, M. R.; Fakhari, S. A. Seyed; Yassemi, S. New classes of set-theoretic complete intersection monomial ideals. (English) Zbl 1360.13054 Commun. Algebra 43, No. 9, 3920-3924 (2015). Reviewer: Eduardo Saenz-de-Cabezon (Logroño) MSC: 13F55 13A15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Kimura, Kyouko; Terai, Naoki; Yoshida, Ken-ichi Arithmetical rank of a squarefree monomial ideal whose Alexander dual is of deviation two. (English) Zbl 1330.13039 Acta Math. Vietnam. 40, No. 3, 375-391 (2015). Reviewer: Thanh Vu (Lincoln) MSC: 13F55 13D02 × Cite Format Result Cite Review PDF Full Text: DOI
Bolognini, Davide; Caminata, Alessio; Macchia, Antonio; Mostafazadehfard, Maral Cohomological dimension and arithmetical rank of some determinantal ideals. (English) Zbl 1329.13026 Matematiche 70, No. 1, 273-300 (2015). Reviewer: Peter Schenzel (Halle) MSC: 13D45 13C40 14B15 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Zhu, Guangjun; Shi, Feng; Gu, Yan Arithmetical rank of the edge ideals of some \(n\)-cyclic graphs with a common edge. (English) Zbl 1342.13017 Turk. J. Math. 39, No. 1, 112-123 (2015). Reviewer: Susan Morey (San Marcos) MSC: 13C15 13A15 13D05 13F55 × Cite Format Result Cite Review PDF Full Text: DOI
Macchia, Antonio The arithmetical rank of the edge ideals of graphs with whiskers. (English) Zbl 1309.13006 Beitr. Algebra Geom. 56, No. 1, 147-158 (2015). Reviewer: S. A. Seyed Fakhari (Tehran) MSC: 13A15 13F55 14M10 05C05 05C38 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kimura, Kyouko; Terai, Naoki Arithmetical rank of Gorenstein squarefree monomial ideals of height three. (English) Zbl 1305.13008 J. Algebra 422, 11-32 (2015). Reviewer: Somayeh Bandari (Tehran) MSC: 13F55 13H10 × Cite Format Result Cite Review PDF Full Text: DOI
Macchia, Antonio On the set-theoretic complete intersection property for the edge ideals of whisker graphs. (English) Zbl 1317.13048 Serdica Math. J. 40, No. 1, 41-54 (2014). Reviewer: Vesselin Drensky (Sofia) MSC: 13F55 14M10 13A15 05C05 05C38 × Cite Format Result Cite Review PDF
Katsabekis, Anargyros On the binomial arithmetical rank of toric ideals. (English) Zbl 1304.14068 J. Algebra Appl. 13, No. 7, Article ID 1450030, 16 p. (2014). Reviewer: Marcel Morales (Saint-Martin-d’Hères) MSC: 14M25 13F20 05C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kimura, Kyouko; Terai, Naoki Binomial arithmetical rank of edge ideals of forests. (English) Zbl 1273.05040 Proc. Am. Math. Soc. 141, No. 6, 1925-1932 (2013). Reviewer: Christos Tatakis (Mitilini) MSC: 05C05 13F55 05C25 × Cite Format Result Cite Review PDF Full Text: DOI
Mohammadi, Fatemeh; Kiani, Dariush On the arithmetical rank of the edge ideals of some graphs. (English) Zbl 1294.13030 Algebra Colloq. 19, Spec. Iss. 1, 797-806 (2012). MSC: 13F20 13F55 13D05 × Cite Format Result Cite Review PDF Full Text: DOI
Varbaro, Matteo On the arithmetical rank of certain Segre embeddings. (English) Zbl 1329.14040 Trans. Am. Math. Soc. 364, No. 10, 5091-5109 (2012). Reviewer: Fernandez Boix (Barcelona) MSC: 14F17 13D45 13D05 14A25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kimura, Kyouko; Rinaldo, Giancarlo; Terai, Naoki Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four. (English) Zbl 1262.13037 Commun. Algebra 40, No. 11, 4147-4170 (2012). Reviewer: Eduardo Saenz-de-Cabezon (Logroño) MSC: 13F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita; Kiani, Dariush; Mohammadi, Fatemeh; Yassemi, Siamak Arithmetical rank of the cyclic and bicyclic graphs. (English) Zbl 1242.13004 J. Algebra Appl. 11, No. 2, 1250039, 14 p. (2012). Reviewer: Marcel Morales (Saint-Martin-d’Hères) MSC: 13A15 13F55 13D02 05C38 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kimura, Kyouko Arithmetical rank of Cohen-Macaulay squarefree monomial ideals of height two. (English) Zbl 1237.13043 J. Commut. Algebra 3, No. 1, 31-46 (2011). MSC: 13F55 13A15 13F20 13H10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Constantinescu, Alexandru; Varbaro, Matteo Koszulness, Krull dimension, and other properties of graph-related algebras. (English) Zbl 1229.05112 J. Algebr. Comb. 34, No. 3, 375-400 (2011). MSC: 05C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kimura, Kyouko; Terai, Naoki; Yoshida, Ken-ichi Schmitt-Vogel type lemma for reductions. (English) Zbl 1230.13006 Arch. Math. 96, No. 6, 535-545 (2011). Reviewer: Trung Dinh (Hanoi) MSC: 13A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Barile, Margherita; Terai, Naoki The Stanley-Reisner ideals of polygons as set-theoretic complete intersections. (English) Zbl 1213.13005 Commun. Algebra 39, No. 2, 621-633 (2011). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13A15 13F55 14M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ene, Viviana; Olteanu, Oana; Terai, Naoki Arithmetical rank of lexsegment edge ideals. (English) Zbl 1224.13026 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 53(101), No. 4, 315-327 (2010). Reviewer: Dorin Popescu (Bucuresti) MSC: 13F55 13A15 55U10 × Cite Format Result Cite Review PDF Full Text: arXiv
Morales, Marcel Simplicial ideals, 2-linear ideals and arithmetical rank. (English) Zbl 1217.13007 J. Algebra 324, No. 12, 3431-3456 (2010). Reviewer: Anargyros Katsabekis (Lamia) MSC: 13F20 13D02 14M99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Katsabekis, Anargyros; Morales, Marcel; Thoma, Apostolos Binomial generation of the radical of a lattice ideal. (English) Zbl 1207.14051 J. Algebra 324, No. 6, 1334-1346 (2010). Reviewer: Mesut Sahin (Çankiri) MSC: 14M25 13F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita; Terai, Naoki Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone. (English) Zbl 1205.13026 Commun. Algebra 38, No. 10, 3686-3698 (2010). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13F55 13A15 14M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Katsabekis, Anargyros Arithmetical rank of toric ideals associated to graphs. (English) Zbl 1200.14104 Proc. Am. Math. Soc. 138, No. 9, 3111-3123 (2010). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 14M25 13F20 05C99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Katsabekis, Anargyros; Thoma, Apostolos Specializations of multigradings and the arithmetical rank of lattice ideals. (English) Zbl 1197.14054 Commun. Algebra 38, No. 5, 1904-1918 (2010). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 14M25 13F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chiang-Hsieh, Hung-Jen Some arithmetic properties of matroidal ideals. (English) Zbl 1189.13010 Commun. Algebra 38, No. 3, 944-952 (2010). MSC: 13C40 13F20 13C13 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita A generalization of a lemma by Schmitt and Vogel. (English) Zbl 1200.13002 Tokyo J. Math. 32, No. 2, 435-440 (2009). Reviewer: Anargyros Katsabekis (Lamia) MSC: 13A15 13F55 14M10 × Cite Format Result Cite Review PDF Full Text: DOI
Kimura, Kyouko; Terai, Naoki; Yoshida, Ken-ichi Arithmetical rank of monomial ideals of deviation two. (English) Zbl 1194.13025 Ene, Viviana (ed.) et al., Combinatorial aspects of commutative algebra. Exploratory workshop on combinatorial commutative algebra and computer algebra, Mangalia, Romania, May 29–31, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4758-9/pbk). Contemporary Mathematics 502, 73-112 (2009). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13F55 13H10 × Cite Format Result Cite Review PDF
Kimura, Kyouko Lyubeznik resolutions and the arithmetical rank of monomial ideals. (English) Zbl 1182.13013 Proc. Am. Math. Soc. 137, No. 11, 3627-3635 (2009). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13E15 13D02 × Cite Format Result Cite Review PDF Full Text: DOI
Kimura, Kyouko; Terai, Naoki; Yoshida, Ken-ichi Arithmetical rank of squarefree monomial ideals of small arithmetic degree. (English) Zbl 1244.13016 J. Algebr. Comb. 29, No. 3, 389-404 (2009). Reviewer: Anne Frühbis-Krüger (Hannover) MSC: 13F55 × Cite Format Result Cite Review PDF Full Text: DOI
Barile, Margherita On the arithmetical rank of a special class of minimal varieties. (English) Zbl 1173.13019 Beitr. Algebra Geom. 50, No. 1, 47-69 (2009). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13D45 14M10 14B15 × Cite Format Result Cite Review PDF Full Text: arXiv EuDML EMIS
Barile, Margherita On the arithmetic rank of an intersection of ideals. (English) Zbl 1157.13001 Algebra Colloq. 15, No. 4, 681-688 (2008). Reviewer: Eduardo Saenz-de-Cabezon (Logroño) MSC: 13A15 13F55 14M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita On the arithmetical rank of the edge ideals of forests. (English) Zbl 1166.13024 Commun. Algebra 36, No. 12, 4678-4703 (2008). Reviewer: Viviana Ene (Constanta) MSC: 13F55 13D02 05C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita Arithmetical ranks of Stanley-Reisner ideals via linear algebra. (English) Zbl 1155.13002 Commun. Algebra 36, No. 12, 4540-4556 (2008). Reviewer: Eduardo Saenz-de-Cabezon (Logroño) MSC: 13A15 13F55 14M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita On ideals generated by monomials and one binomial. (English) Zbl 1140.13003 Algebra Colloq. 14, No. 4, 631-638 (2007). Reviewer: Michael Hellus (Leipzig) MSC: 13A10 14M10 13E15 14F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita Almost set-theoretic complete intersections in characteristic zero. (English) Zbl 1125.14028 Collect. Math. 58, No. 1, 61-72 (2007). Reviewer: Anargyros Katsabekis (Nicosia) MSC: 14M10 14M25 20M05 × Cite Format Result Cite Review PDF Full Text: arXiv EuDML
Katsabekis, Anargyros; Thoma, Apostolos Matchings in simplicial complexes, circuits and toric varieties. (English) Zbl 1115.13029 J. Comb. Theory, Ser. A 114, No. 2, 300-310 (2007). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 13F55 14M25 × Cite Format Result Cite Review PDF Full Text: DOI
Barile, Margherita On a special class of simplicial toric varieties. (English) Zbl 1115.14040 J. Algebra 308, No. 1, 368-382 (2007). Reviewer: Marcel Morales (Saint-Martin-d’Heres) MSC: 14M10 14M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita A note on monomial ideals. (English) Zbl 1112.13001 Arch. Math. 87, No. 6, 516-521 (2006). Reviewer: Mihai Cipu (Bucureşti) MSC: 13A10 13A15 13F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barile, Margherita On toric varieties of high arithmetical rank. (English) Zbl 1099.14051 Yokohama Math. J. 52, No. 2, 125-130 (2006). Reviewer: Edoardo Ballico (Povo) MSC: 14R99 14M25 19F27 × Cite Format Result Cite Review PDF Full Text: arXiv
Barile, Margherita On ideals whose radical is a monomial ideal. (English) Zbl 1098.13023 Commun. Algebra 33, No. 12, 4479-4490 (2005). Reviewer: Ali Benhissi (Monastir) MSC: 13F20 13A10 13A15 13E15 × Cite Format Result Cite Review PDF Full Text: DOI
Barile, Margherita On the computation of arithmetical ranks. (English) Zbl 1079.13004 Int. J. Pure Appl. Math. 17, No. 2, 143-161 (2004). Reviewer: Moshe Roitman (Haifa) MSC: 13A15 13E15 × Cite Format Result Cite Review PDF
Kalinowski, Jozef On rank equivalence and rank preserving operators. (English) Zbl 1274.15001 Novi Sad J. Math. 32, No. 1, 133-139 (2002). MSC: 15A03 15A86 × Cite Format Result Cite Review PDF
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Barile, Margherita; Morales, Marcel; Thoma, Apostolos On simplicial toric varieties which are set-theoretic complete intersections. (English) Zbl 0971.14041 J. Algebra 226, No. 2, 880-892 (2000). Reviewer: Giorgio Bolondi (Milano) MSC: 14M25 14M10 × Cite Format Result Cite Review PDF Full Text: DOI
Thoma, Apostolos On the binomial arithmetical rank. (English) Zbl 1033.14014 Arch. Math. 74, No. 1, 22-25 (2000). MSC: 14H05 14M10 13A10 × Cite Format Result Cite Review PDF Full Text: DOI
Yan, Zhao Minimal resultant systems. (English) Zbl 0979.13011 J. Algebra 216, No. 1, 105-123 (1999). MSC: 13C40 13D02 × Cite Format Result Cite Review PDF Full Text: DOI
Noui, Lemnouar Transvectors of rank 8 over an algebraically closed field. (Transvecteur de rang 8 sur un corps algébriquement clos.) (French) Zbl 0872.15023 C. R. Acad. Sci., Paris, Sér. I 324, No. 6, 611-614 (1997). MSC: 15A72 × Cite Format Result Cite Review PDF Full Text: DOI
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Bruns, Winfried; Schwänzl, Roland The number of equations defining a determinantal variety. (English) Zbl 0725.14039 Bull. Lond. Math. Soc. 22, No. 5, 439-445 (1990). Reviewer: P.Schenzel (Halle) MSC: 14M12 14M10 14F20 13D05 × Cite Format Result Cite Review PDF Full Text: DOI
Bruns, Winfried Additions to the theory of algebras with straightening law. (English) Zbl 0731.13014 Commutative algebra, Proc. Microprogram, Berkeley/CA (USA) 1989, Publ., Math. Sci. Res. Inst. 15, 111-138 (1989). Reviewer: F.Théron (Pretoria) MSC: 13F50 × Cite Format Result Cite Review PDF
Lyubeznik, Gennady A survey of problems and results on the number of defining equations. (English) Zbl 0753.14001 Commutative algebra, Proc. Microprogram, Berkeley/CA (USA) 1989, Publ., Math. Sci. Res. Inst. 15, 375-390 (1989). Reviewer: H.Matsumura (Fukuoka) MSC: 14A05 14M10 13D45 × Cite Format Result Cite Review PDF
Khisamiev, N. G. Arithmetic hierarchy of Abelian groups. (English. Russian original) Zbl 0679.20047 Sib. Math. J. 29, No. 6, 987-999 (1988); translation from Sib. Mat. Zh. 29, No. 6(172), 144-159 (1988). MSC: 20K25 20A15 03D55 20K20 × Cite Format Result Cite Review PDF Full Text: DOI
Khisamiev, N. G. Arithmetical hierarchy of Abelian groups. (Russian) Zbl 0675.20043 Sib. Mat. Zh. 29, No. 6(172), 144-159 (1988). Reviewer: St.Balcerzyk MSC: 20K25 20A15 03D55 20K20 × Cite Format Result Cite Review PDF Full Text: EuDML
Jaballah, Ali Monomiale Ideale und mengentheoretische vollständige Durchschnitte. (Monomial ideals and set theoretical complete intersections). (German) Zbl 0656.13023 Arch. Math. 51, No. 4, 308-312 (1988). Reviewer: K.Kiyek MSC: 13F20 13A15 14M10 × Cite Format Result Cite Review PDF Full Text: DOI
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Gräbe, Hans-Gert Über den arithmetischen Rang quadratfreier Potenzproduktideale. (German) Zbl 0562.13016 Math. Nachr. 120, 217-227 (1985). Reviewer: L.Bădescu MSC: 13F20 14M10 13E15 13D03 × Cite Format Result Cite Review PDF Full Text: DOI
Matsuda, Ryuki Torsion-free Abelian semigroup rings. V. (English) Zbl 0414.13003 Bull. Fac. Sci., Ibaraki Univ., Ser. A 11, 1-37 (1979). MSC: 13B25 13E15 13F05 13C15 20M25 × Cite Format Result Cite Review PDF Full Text: DOI