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Journal articles on the topic 'Macaulay 2'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Frühbis-Krüger, Anne, and Alexander Neumer. "Simple Cohen–Macaulay Codimension 2 Singularities." Communications in Algebra 38, no. 2 (February 12, 2010): 454–95. http://dx.doi.org/10.1080/00927870802606018.

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2

MCKELVY, WILLIAM R. "TWO UNPUBLISHED MACAULAY LETTERS." Notes and Queries 45, no. 2 (June 1, 1998): 215–16. http://dx.doi.org/10.1093/nq/45-2-215.

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3

Smith, Larry. "Some Rings of Invariants that are Cohen-Macaulay." Canadian Mathematical Bulletin 39, no. 2 (June 1, 1996): 238–40. http://dx.doi.org/10.4153/cmb-1996-030-2.

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AbstractLet be a representation of the finite group G over the field . If the order |G| of G is relatively prime to the characteristic of or n = 1 or 2, then it is known that the ring of invariants is Cohen-Macaulay. There are examples to show that need not be Cohen-Macaulay when |G| is divisible by the characteristic of . In all such examples is at least 4. In this note we fill the gap between these results and show that rings of invariants in three variables are always Cohen-Macaulay.

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4

Hong Loan, Nguyen. "On certain invariants of idealizations." Studia Scientiarum Mathematicarum Hungarica 51, no. 3 (September 1, 2014): 357–65. http://dx.doi.org/10.1556/sscmath.51.2014.3.1288.

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Let (R, m) be a Noetherian local ring and M a finitely generated R-module. In this paper, we study some invariants of the idealization R ⋉ M of R and M such as the polynomial type introduced by Cuong [2] and the polynomial type of fractions introduced by Cuong-Minh [3]. As consequences, we characterize the Cohen-Macaulay, generalized Cohen-Macaulay, pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay properties of the idealization R ⋉ M.

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5

Naeem, Muhammad. "Cohen–Macaulay monomial ideals of codimension 2." manuscripta mathematica 127, no. 4 (October 16, 2008): 533–45. http://dx.doi.org/10.1007/s00229-008-0217-4.

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6

Hoang, Do Trong, Giancarlo Rinaldo, and Naoki Terai. "Cohen-Macaulay and (S2) Properties of the Second Power of Squarefree Monomial Ideals." Mathematics 7, no. 8 (July 31, 2019): 684. http://dx.doi.org/10.3390/math7080684.

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We show that Cohen-Macaulay and (S 2 ) properties are equivalent for the second power of an edge ideal. We give an example of a Gorenstein squarefree monomial ideal I such that S / I 2 satisfies the Serre condition (S 2 ), but is not Cohen-Macaulay.

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7

Jafari, Madineh, Amir Mafi, and Hero Saremi. "Sequentially cohen-macaulay matroidal ideals." Filomat 34, no. 13 (2020): 4233–44. http://dx.doi.org/10.2298/fil2013233j.

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Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroidal ideal of degree d in R. Our main focus is determining when matroidal ideals are sequentially Cohen- Macaulay. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree 2 are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree d ? 3 in some special cases.

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8

Ballhatchet, Kenneth. "The importance of Macaulay." Journal of the Royal Asiatic Society of Great Britain & Ireland 122, no. 1 (January 1990): 91–94. http://dx.doi.org/10.1017/s0035869x00107877.

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In J.R.A.S. 1988/2 Robert E. Frykenberg assails what he calls the “myth” that Macaulay's minute on education in British India was the occasion for a radical change in policy which imposed English education on an unwilling people. He puts forward three main arguments. First, there was no radical change in policy, for the government continued to support “Oriental” education and scholarship as well as English education. Secondly, Macaulay's advocacy of English education was a recognition of the views of “forward-looking gentry in India”. Thirdly, his minute was “one more salvo in a long and running set of encounters in which the positions of some protagonists were often much more blurred than has been properly realised by later generations of historians”. What is new in all this?

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9

HOLM, HENRIK. "THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS." Glasgow Mathematical Journal 59, no. 3 (June 10, 2016): 549–61. http://dx.doi.org/10.1017/s0017089516000343.

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AbstractOver a Cohen–Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module, in the sense of Hochster, can be written as a direct limit of small CM modules. In analogy with Govorov and Lazard's characterization of flat modules as direct limits of finitely generated free modules, one can view this as a “structure theorem” for balanced big CM modules. (2) Every finitely generated module has a pre-envelope with respect to the class of finitely generated maximal CM modules. This result is, in some sense, dual to the existence of maximal CM approximations, which has been proved by Auslander and Buchweitz.

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10

Hiramatsu, Naoya. "Degenerations of graded Cohen-Macaulay modules." Journal of Commutative Algebra 7, no. 2 (June 2015): 221–39. http://dx.doi.org/10.1216/jca-2015-7-2-221.

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11

Taniguchi, Naoki, Tran Thi Phuong, Nguyen Thi Dung, and Tran Nguyen An. "Topics on sequentially Cohen-Macaulay modules." Journal of Commutative Algebra 10, no. 2 (April 2018): 295–304. http://dx.doi.org/10.1216/jca-2018-10-2-295.

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12

Ragusa, Alfio, and Giuseppe Zappalà. "On Complete Intersections Contained in Cohen-Macaulay and Gorenstein Ideals." Algebra Colloquium 18, spec01 (December 2011): 857–72. http://dx.doi.org/10.1142/s1005386711000745.

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We look for complete intersections containing certain arithmetically Cohen-Macaulay schemes, and give a complete description in the case of 2-codimensional arithmetically Cohen-Macaulay schemes and 3-codimensional arithmetically Gorenstein schemes. In particular, we prove that in these cases the sets of types of complete intersections containing such schemes have a unique minimal element and we compute it.

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13

Alonso, María Emilia, Maria Grazia Marinari, and Teo Mora. "The big Mother of all dualities 2: Macaulay bases." Applicable Algebra in Engineering, Communication and Computing 17, no. 6 (November 21, 2006): 409–51. http://dx.doi.org/10.1007/s00200-006-0019-4.

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14

Björner, Anders, Michelle Wachs, and Volkmar Welker. "On sequentially Cohen-Macaulay complexes and posets." Israel Journal of Mathematics 169, no. 1 (November 22, 2008): 295–316. http://dx.doi.org/10.1007/s11856-009-0012-2.

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15

Denizler, I. H., and R. Y. Sharp. "Co-Cohen-Macaulay Artinian modules over commutative rings." Glasgow Mathematical Journal 38, no. 3 (September 1996): 359–66. http://dx.doi.org/10.1017/s0017089500031797.

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In [7], Z. Tang and H. Zakeri introduced the concept of co-Cohen-Macaulay Artinian module over a quasi-local commutative ring R (with identity): a non-zero Artinian R-module A is said to be a co-Cohen-Macaulay module if and only if codepth A = dim A, where codepth A is the length of a maximalA-cosequence and dimA is the Krull dimension of A as defined by R. N. Roberts in [2]. Tang and Zakeriobtained several properties of co-Cohen-Macaulay Artinian R-modules, including a characterization of such modules by means of the modules of generalized fractions introduced by Zakeri and the present second author in [6]; this characterization is explained as follows.

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16

Favacchio, Giuseppe, Elena Guardo, and Beatrice Picone. "Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1." Journal of Algebra and Its Applications 18, no. 04 (March 25, 2019): 1950073. http://dx.doi.org/10.1142/s0219498819500737.

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In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

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17

Walter, Charles H. "Hyperplane sections of arithmetically Cohen-Macaulay curves." Proceedings of the American Mathematical Society 123, no. 9 (September 1, 1995): 2651. http://dx.doi.org/10.1090/s0002-9939-1995-1260185-2.

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18

Cueva-Zepeda, Alfredo. "Deflection of stepped shafts using Macaulay functions." Computer Applications in Engineering Education 4, no. 2 (1996): 109–15. http://dx.doi.org/10.1002/(sici)1099-0542(1996)4:2<109::aid-cae2>3.0.co;2-h.

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19

Nadi, Parvaneh, Farhad Rahmati, and Majid Eghbali. "Lyubeznik tables of linked ideals." Journal of Algebra and Its Applications 19, no. 07 (August 30, 2019): 2050138. http://dx.doi.org/10.1142/s0219498820501388.

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In this paper, we examine the Lyubeznik tables of two linked ideals [Formula: see text] and [Formula: see text] of a complete regular local ring [Formula: see text] containing a field. More precisely, we prove that the Lyubeznik tables of two evenly linked ideals [Formula: see text] and [Formula: see text] are the same when [Formula: see text] and [Formula: see text] both satisfy one of the following properties: (1) canonically Cohen–Macaulay, (2) generalized Cohen–Macaulay and (3) Buchsbaum. Furthermore, we give some conditions for equality of Lyubeznik tables of two linked ideals of dimension 2.

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20

Cuong, Nguyen Tu, Nguyen Tuan Long, and Hoang Le Truong. "Uniform Bounds in Sequentially Generalized Cohen–Macaulay Modules." Vietnam Journal of Mathematics 43, no. 2 (February 15, 2015): 343–56. http://dx.doi.org/10.1007/s10013-015-0126-2.

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21

Stillman, Michael. "Computing in algebraic geometry and commutative algebra using Macaulay 2." Journal of Symbolic Computation 36, no. 3-4 (September 2003): 595–611. http://dx.doi.org/10.1016/s0747-7171(03)00096-8.

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22

Qin, Xiaoshan, Yanhua Wang, and James Zhang. "Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity." Frontiers of Mathematics in China 14, no. 5 (October 2019): 923–40. http://dx.doi.org/10.1007/s11464-019-0793-5.

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23

Wang, Hsin-Ju. "On Cohen–Macaulay Local Rings with Embedding Dimensione+d−2." Journal of Algebra 190, no. 1 (April 1997): 226–40. http://dx.doi.org/10.1006/jabr.1996.6894.

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24

Verma, J. K. "Joint reductions and Rees algebras." Mathematical Proceedings of the Cambridge Philosophical Society 109, no. 2 (March 1991): 335–42. http://dx.doi.org/10.1017/s0305004100069796.

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Let R be a Cohen-Macaulay local ring of dimension d, multiplicity e and embedding dimension v. Abhyankar [1] showed that v − d + 1 ≤ e. When equality holds, R is said to have minimal multiplicity. The purpose of this paper is to study the preservation of this property under the formation of Rees algebras of several ideals in a 2-dimensional Cohen-Macaulay (CM for short) local ring. Our main tool is the theory of joint reductions and mixed multiplicities developed by Rees [9] and Teissier[12].

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25

Riley, Adrian M., Rodney Y. Sharp, and Hossein Zakeri. "Cousin complexes and generalized fractions." Glasgow Mathematical Journal 26, no. 1 (January 1985): 51–67. http://dx.doi.org/10.1017/s0017089500005772.

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Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [6, §2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n≥0,Cohen-Macaulay rings may be characterized in terms of the Cousin complex: A is a Cohen-Macaulay ring if and only if C(A) is exact [6, (4.7)]. Also the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring: see [6, (5.4)].

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26

Drozd, Yu, G. M. Greuel, and I. Kashuba. "On Cohen—Macaulay Modules on Surface Singularities." Moscow Mathematical Journal 3, no. 2 (2003): 397–418. http://dx.doi.org/10.17323/1609-4514-2003-3-2-397-418.

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27

Takahashi, Ryo, and Yuji Yoshino. "Characterizing Cohen-Macaulay local rings by Frobenius maps." Proceedings of the American Mathematical Society 132, no. 11 (May 12, 2004): 3177–87. http://dx.doi.org/10.1090/s0002-9939-04-07525-2.

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28

BAUR, KARIN, DUSKO BOGDANIC, and ANA GARCIA ELSENER. "CLUSTER CATEGORIES FROM GRASSMANNIANS AND ROOT COMBINATORICS." Nagoya Mathematical Journal 240 (June 3, 2019): 322–54. http://dx.doi.org/10.1017/nmj.2019.14.

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The category of Cohen–Macaulay modules of an algebra $B_{k,n}$ is used in Jensen et al. (A categorification of Grassmannian cluster algebras, Proc. Lond. Math. Soc. (3) 113(2) (2016), 185–212) to give an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$-planes in $n$-space. In this paper, we find canonical Auslander–Reiten sequences and study the Auslander–Reiten translation periodicity for this category. Furthermore, we give an explicit construction of Cohen–Macaulay modules of arbitrary rank. We then use our results to establish a correspondence between rigid indecomposable modules of rank 2 and real roots of degree 2 for the associated Kac–Moody algebra in the tame cases.

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29

Wall, C. T. C. "Quartic curves in characteristic 2." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 3 (May 1995): 393–414. http://dx.doi.org/10.1017/s0305004100073254.

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Simple singularities in positive characteristicSimple singularities in positive characteristic have been discussed by many authors, and the article [5] in particular establishes the subject on a firm footing. In it a simple, or ‘ADE’ singularity is defined by a list of normal forms and it is shown that the following conditions on a singularity are equivalent: (i) it is simple, (ii) it has finite deformation type, (iii) it has finite Cohen-Macaulay module type. Moreover, the normal forms for surface singularities coincide with the earlier list of Artin [1] and those for curves with the list of [9]: in those papers further characterizations were obtained.

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30

Gao, Nan. "The relative transpose over Cohen-Macaulay finite Artin algebras." Chinese Annals of Mathematics, Series B 30, no. 3 (April 16, 2009): 231–38. http://dx.doi.org/10.1007/s11401-008-0227-2.

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31

Sharp, R. Y., and M. Yassi. "Generalized fractions and Hughes' gradetheoretic analogue of the Cousin complex." Glasgow Mathematical Journal 32, no. 2 (May 1990): 173–88. http://dx.doi.org/10.1017/s0017089500009198.

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Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [19, Section 2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n ∈ N0 (we use N0 to denote the set of non-negative integers),Cohen–Macaulay rings can be characterized in terms of the Cousin complex: A is a Cohen–Macaulay ring if and only if C(A) is exact [19, (4.7)]. Also, the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring (see [19,(5.4)]).

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32

KIANI, DARIUSH, SARA SAEEDI MADANI, and NAOKI TERAI. "GORENSTEIN AND Sr PATH IDEALS OF CYCLES." Glasgow Mathematical Journal 57, no. 1 (August 26, 2014): 7–15. http://dx.doi.org/10.1017/s0017089514000111.

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AbstractLet R = k[x1,…,xn], where k is a field. The path ideal (of length t ≥ 2) of a directed graph G is the monomial ideal, denoted by It(G), whose generators correspond to the directed paths of length t in G. Let Cn be an n-cycle. We show that R/It(Cn) is Sr if and only if it is Cohen-Macaulay or $\lceil \frac{n}{n-t-1}\rceil\geq r+3$. In addition, we prove that R/It(Cn) is Gorenstein if and only if n = t or 2t + 1. Also, we determine all ordinary and symbolic powers of It(Cn) which are Cohen-Macaulay. Finally, we prove that It(Cn) has a linear resolution if and only if t ≥ n − 2.

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33

Se, Tony, and J. Grant Serio. "The Cohen-Macaulay property of affine semigroup rings in dimension 2." Communications in Algebra 47, no. 7 (January 19, 2019): 2979–94. http://dx.doi.org/10.1080/00927872.2018.1546392.

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34

Chiantini, Luca, and Daniele Faenzi. "Rank 2 arithmetically Cohen-Macaulay bundles on a general quintic surface." Mathematische Nachrichten 282, no. 12 (November 27, 2009): 1691–708. http://dx.doi.org/10.1002/mana.200610825.

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35

Ballico, E. "Rank 2 totally arithmetically Cohen–Macaulay vector bundles on Hirzebruch surfaces." Annali di Matematica Pura ed Applicata 188, no. 4 (November 27, 2008): 603–9. http://dx.doi.org/10.1007/s10231-008-0091-4.

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36

Faenzi, Daniele. "Rank 2 arithmetically Cohen–Macaulay bundles on a nonsingular cubic surface." Journal of Algebra 319, no. 1 (January 2008): 143–86. http://dx.doi.org/10.1016/j.jalgebra.2007.10.005.

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37

Frühbis-Krüger, Anne, and Matthias Zach. "On the vanishing topology of isolated Cohen–Macaulay codimension 2 singularities." Geometry & Topology 25, no. 5 (September 3, 2021): 2167–94. http://dx.doi.org/10.2140/gt.2021.25.2167.

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38

Cumming, Christine. "The core of an ideal in Cohen-Macaulay rings." Journal of Commutative Algebra 10, no. 2 (April 2018): 163–70. http://dx.doi.org/10.1216/jca-2018-10-2-163.

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39

Beorchia, Valentina, Paolo Lella, and Enrico Schlesinger. "The Maximum Genus Problem for Locally Cohen-Macaulay Space Curves." Milan Journal of Mathematics 86, no. 2 (September 1, 2018): 137–55. http://dx.doi.org/10.1007/s00032-018-0284-2.

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40

Beccace, Francesca, Roberto Tasca, and Luisa Tibiletti. "The Macaulay Duration: A Key Indicator for the Risk-Adjustment in Fair Value." International Journal of Business and Management 13, no. 12 (November 21, 2018): 251. http://dx.doi.org/10.5539/ijbm.v13n12p251.

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International Financial Reporting Standards (IFRS) 13 Fair Value Measurement lays down two methods to adjust Expected Present Value (EPV) for risk. According to Method 1, expected cash inflows should be risk-adjusted by subtracting a risk-premium and discounted at the market risk-free rate, see (IFRS 13, B25). In contrast according to Method 2, expected cash inflows should be discounted at the risk-free rate augmented by a risk-premium addendum, see (IFRS 13, B26). Standard IFRS 13, B29 leaves the freedom to choose between the two methods. The aim of this note is to identify the relationship between the Risk-Adjusted EPVs rolled out from Method 1 and Method 2. First we introduce a theoretical solution to risk-adjustments compliant with the Standard IFRS 13, B29. Then, we set up a user-oriented proxy to connect the risk-premium present in Method 1 with the risk-adjusted rate present in Method 2. This proxy spots light on the key role played by the Macaulay Duration of expected inflows, rather than that of the lifetime of the project. As a consequence, projects expiring at the same redemption date and endowed with the same EPV and/or the same total inflow may differ considerably in risk-adjustments, due to different Macaulay Durations. A user-oriented method to properly to fast evaluate risk-adjustments for multi-cash inflow projects is provided. Sensitivity analysis of the impact of the Macaulay Duration on Risk-Adjusted EPV is also rolled out through numerical examples.

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41

Mafi, Amir. "Co-Cohen-Macaulay Modules and Generalized Local Cohomology." Algebra Colloquium 18, spec01 (December 2011): 807–13. http://dx.doi.org/10.1142/s100538671100068x.

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Let (R,𝔪) be a Noetherian local ring, 𝔞 a proper ideal of R, and M, N two finitely generated R-modules of finite projective dimension m and of finite dimension n, respectively. It is shown that if n ≤ 2, then the generalized local cohomology module [Formula: see text] is a co-Cohen-Macaulay module. Additionally, we show that [Formula: see text] for all i > m+s and [Formula: see text], where s is the cohomological dimension of N with respect to 𝔞.

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42

Saeedi Madani, Sara, and Dariush Kiani. "Cohen-Macaulay and Gorenstein Path Ideals of Trees." Algebra Colloquium 23, no. 03 (June 20, 2016): 469–80. http://dx.doi.org/10.1142/s1005386716000456.

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Let R=k[x1,…,xn], where k is a field. The path ideal (of length t ≥ 2) of a directed graph G is the monomial ideal, denoted by It(G), whose generators correspond to the directed paths of length t in G. Let Γ be a directed rooted tree. We characterize all such trees whose path ideals are unmixed and Cohen-Macaulay. Moreover, we show that R/It(Γ) is Gorenstein if and only if the Stanley-Reisner simplicial complex of It(Γ) is a matroid.

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43

Johnston, Bernard L., and Jugal Verma. "On the length formula of Hoskin and Deligne and associated graded rings of two-dimensional regular local rings." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 3 (May 1992): 423–32. http://dx.doi.org/10.1017/s0305004100075526.

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Let (R, m) be a 2-dimensional regular local ring and I an m-primary ideal. The aim of this paper is to find conditions on I so that the associated graded ring of I,and the Rees ring of I,where t is an indeterminate, are Cohen–Macaulay (resp. Gorenstein). To this end, we use the results and techniques from Zariski's theory of complete ideals ([14], appendix 5) and its later generalizations and refinements due to Huneke [7] and Lipman[8]. The main result is an application of three deep theorems: (i) a generalization of Macaulay's classical theorem on Hilbert series of Gorenstein graded rings [13], (ii) a generalization of the Briançon–Skoda theorem due to Lipman and Sathaye [9], and (iii) a formula for the length of R/I, where I is a complete m-primary ideal, due to Hoskin[4] and Deligne[1].

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44

Hassler, Wolfgang, Ryan Karr, Lee Klingler, and Roger Wiegand. "Indecomposable modules of large rank over Cohen-Macaulay local rings." Transactions of the American Mathematical Society 360, no. 03 (March 1, 2008): 1391–407. http://dx.doi.org/10.1090/s0002-9947-07-04226-2.

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45

Hyry, Eero. "Coefficient ideals and the Cohen-Macaulay property of Rees algebras." Proceedings of the American Mathematical Society 129, no. 5 (October 24, 2000): 1299–308. http://dx.doi.org/10.1090/s0002-9939-00-05673-2.

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46

Yanagawa, Kohji. "Higher Cohen-Macaulay property of squarefree modules and simplicial posets." Proceedings of the American Mathematical Society 139, no. 09 (September 1, 2011): 3057. http://dx.doi.org/10.1090/s0002-9939-2011-10734-2.

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47

King, Simon A., David Green, and Graham Ellis. "The mod–2 cohomology ring of the third Conway group is Cohen–Macaulay." Algebraic & Geometric Topology 11, no. 2 (March 11, 2011): 719–34. http://dx.doi.org/10.2140/agt.2011.11.719.

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48

Baciu, C., V. Ene, G. Pfister, and D. Popescu. "Rank 2 Cohen–Macaulay modules over singularities of type x13+x23+x33+x43." Journal of Algebra 292, no. 2 (October 2005): 447–91. http://dx.doi.org/10.1016/j.jalgebra.2005.01.001.

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49

Laza, Radu, Gerhard Pfister, and Dorin Popescu. "Maximal Cohen–Macaulay modules over the cone of an elliptic curve." Journal of Algebra 253, no. 2 (July 2002): 209–36. http://dx.doi.org/10.1016/s0021-8693(02)00052-2.

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50

Garcia Elsener, A. "Gentle m-Calabi-Yau tilted algebras." Algebra and Discrete Mathematics 30, no. 1 (2020): 44–62. http://dx.doi.org/10.12958/adm1423.

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We prove that all gentle 2-Calabi-Yau tilted algebras are Jacobian, moreover their bound quiver can be obtained via block decomposition. For two related families, the m-cluster-tilted algebras of type A and A~, we prove that a module M is stable Cohen-Macaulay if and only if Ωm+1τM≃M.

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