Journal articles: 'Minimal generators'

1

Porst, Hans-E. "Varieties without minimal generators." Algebra Universalis 45, no. 1 (February 1, 2001): 23–33. http://dx.doi.org/10.1007/s000120050199.

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2

Kowalski, Zbigniew. "Minimal generators for ergodic endomorphisms." Studia Mathematica 91, no. 2 (1988): 85–88. http://dx.doi.org/10.4064/sm-91-2-85-88.

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3

Zaman, Naveed. "Minimal Generators and Injective Modules." Communications in Algebra 31, no. 2 (January 4, 2003): 869–81. http://dx.doi.org/10.1081/agb-120017348.

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4

Leavitt, W. G., and R. F. Rossa. "Minimal generators of radical classes." Communications in Algebra 14, no. 3 (January 1986): 531–55. http://dx.doi.org/10.1080/00927878608823324.

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5

Hillar, Christopher J., and Troels Windfeldt. "Minimal generators for symmetric ideals." Proceedings of the American Mathematical Society 136, no. 12 (June 11, 2008): 4135–37. http://dx.doi.org/10.1090/s0002-9939-08-09427-6.

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6

Lucchini, Andrea. "Generators and minimal normal subgroups." Archiv der Mathematik 64, no. 4 (April 1995): 273–76. http://dx.doi.org/10.1007/bf01198079.

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Vimieiro, Renato, and Pablo Moscato. "Mining disjunctive minimal generators with TitanicOR." Expert Systems with Applications 39, no. 9 (July 2012): 8228–38. http://dx.doi.org/10.1016/j.eswa.2012.01.141.

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8

Conaway, Rebecca, Felix Gotti, Jesse Horton, Christopher O’Neill, Roberto Pelayo, Mesa Pracht, and Brian Wissman. "Minimal presentations of shifted numerical monoids." International Journal of Algebra and Computation 28, no. 01 (February 2018): 53–68. http://dx.doi.org/10.1142/s0218196718500030.

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A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid [Formula: see text], consider the family of “shifted” monoids [Formula: see text] obtained by adding [Formula: see text] to each generator of [Formula: see text]. In this paper, we examine minimal relations among the generators of [Formula: see text] when [Formula: see text] is sufficiently large, culminating in a description that is periodic in the shift parameter [Formula: see text]. We explore several applications to computation and factorization theory, and improve a recent result of Thanh Vu from combinatorial commutative algebra.

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9

Fang, Y. P., K. W. Meng, and X. Q. Yang. "On minimal generators for semi-closed polyhedra." Optimization 64, no. 4 (August 6, 2013): 761–70. http://dx.doi.org/10.1080/02331934.2013.820299.

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10

Burckel, Serge, and Marianne Morillon. "Three generators for minimal writing-space computations." RAIRO - Theoretical Informatics and Applications 34, no. 2 (March 2000): 131–38. http://dx.doi.org/10.1051/ita:2000110.

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11

Litovsky, I. "Minimal generators of submonoids of $A^\infty $." RAIRO - Theoretical Informatics and Applications 25, no. 1 (1991): 3–17. http://dx.doi.org/10.1051/ita/1991250100031.

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12

HAMROUNI, TAREK, SADOK BEN YAHIA, and ENGELBERT MEPHU NGUIFO. "SUCCINCT MINIMAL GENERATORS: THEORETICAL FOUNDATIONS AND APPLICATIONS." International Journal of Foundations of Computer Science 19, no. 02 (April 2008): 271–96. http://dx.doi.org/10.1142/s0129054108005681.

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In data mining applications, highly sized contexts are handled what usually results in a considerably large set of frequent itemsets, even for high values of the minimum support threshold. An interesting solution consists then in applying an appropriate closure operator that structures frequent itemsets into equivalence classes, such that two itemsets belong to the same class if they appear in the same sets of objects. Among equivalent itemsets, minimal elements (w.r.t. the number of items) are called minimal generators (MGs), while their associated closure is called closed itemset (CI), and is the largest one within the corresponding equivalence class. Thus, the pairs - composed by MGs and their associated CIs - make easier localizing each itemset since it is necessarily encompassed by an MG and an CI. In addition, they offer informative implication/association rules, with minimal premises and maximal conclusions, which losslessly represent the entire rule set. These important concepts - MG and CI - were hence at the origin of various works. Nevertheless, the inherent absence of a unique MG associated to a given CI leads to an intra-class combinatorial redundancy that leads an exhaustive storage and impractical use. This motivated an in-depth study towards a lossless reduction of this redundancy. This study was started by Dong et al. who introduced the succinct system of minimal generators (SSMG) as an attempt to eliminate the redundancy within this set. In this paper, we give a thorough study of the SSMG as formerly defined by Dong et al. This system will be shown to suffer from some flaws. As a remedy, we introduce a new lossless reduction of the MG set allowing to overcome its limitations. The new SSMG will then be incorporated into the framework of generic bases of association rules. This makes it possible to only maintain succinct and informative rules. After that, we give a thorough formal study of the related inference mechanisms allowing to derive all redundant association rules, starting from the maintained ones. Finally, an experimental evaluation shows the utility of our approach towards eliminating important rate of redundant information.

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13

Kubjas, Kaie. "Low degree minimal generators of phylogenetic semigroups." European Journal of Mathematics 1, no. 1 (December 13, 2014): 2–24. http://dx.doi.org/10.1007/s40879-014-0011-7.

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14

Reyes, Enrique, Christos Tatakis, and Apostolos Thoma. "Minimal generators of toric ideals of graphs." Advances in Applied Mathematics 48, no. 1 (January 2012): 64–78. http://dx.doi.org/10.1016/j.aam.2011.06.003.

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15

GHANE, F. H., and M. SALEH. "C1-ROBUSTLY MINIMAL IFS WITH THREE GENERATORS." International Journal of Bifurcation and Chaos 20, no. 10 (October 2010): 3373–77. http://dx.doi.org/10.1142/s0218127410027775.

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We provide an iterated function system on any compact connected m-dimensional manifold with just three diffeomorphisms which are C1-robustly minimal. This improves the main result of [Ghane et al., 2010].

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16

Kim, Henry H. "Minimal generators of the ideal class group." Journal of Number Theory 222 (May 2021): 157–67. http://dx.doi.org/10.1016/j.jnt.2020.12.001.

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17

Pappalardi, Francesco. "On Minimal Sets of Generators for Primitive Roots." Canadian Mathematical Bulletin 38, no. 4 (December 1, 1995): 465–68. http://dx.doi.org/10.4153/cmb-1995-068-4.

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AbstractA conjecture of Brown and Zassenhaus (see [2]) states that the first log/? primes generate a primitive root (mod p) for almost all primes p. As a consequence of a Theorem of Burgess and Elliott (see [3]) it is easy to see that the first log2p log log4+∊p primes generate a primitive root (mod p) for almost all primes p. We improve this showing that the first log2p/ log log p primes generate a primitive root (mod p) for almost all primes p.

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18

Briales, E., A. Campillo, C. Marijuán, and P. Pisón. "Minimal systems of generators for ideals of semigroups." Journal of Pure and Applied Algebra 124, no. 1-3 (February 1998): 7–30. http://dx.doi.org/10.1016/s0022-4049(96)00106-5.

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19

Heyne, Gregor, Michael Kupper, and Christoph Mainberger. "Minimal supersolutions of BSDEs with lower semicontinuous generators." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 50, no. 2 (May 2014): 524–38. http://dx.doi.org/10.1214/12-aihp523.

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20

Leavitt, W. G. "A note on minimal generators of hereditary radicals." Periodica Mathematica Hungarica 19, no. 1 (March 1988): 41–47. http://dx.doi.org/10.1007/bf01848007.

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21

Cioffi, F., M. G. Marinari, and L. Ramella. "Regularity bounds by minimal generators and Hilbert function." Collectanea mathematica 60, no. 1 (February 2009): 89–100. http://dx.doi.org/10.1007/bf03191218.

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22

Goldstein, Dmitry, and Naum Krupnik. "Minimal number of idempotent generators for certain algebras." Integral Equations and Operator Theory 37, no. 1 (March 2000): 20–31. http://dx.doi.org/10.1007/bf01673620.

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23

Dutta, S. P. "On modules of finite projective dimension." Nagoya Mathematical Journal 219 (September 2015): 87–111. http://dx.doi.org/10.1017/s0027763000027100.

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AbstractWe address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ringRof mixed characteristicp> 0, wherepis a nonzero divisor, ifIis an ideal of finite projective dimension overRandp𝜖Iorpis a nonzero divisor onR/I, then every minimal generator ofIis a nonzero divisor. Hence, ifPis a prime ideal of finite projective dimension in a local ringR, then every minimal generator ofPis a nonzero divisor inR.

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24

Lishak, Boris. "Balanced finite presentations of the trivial group." Journal of Topology and Analysis 09, no. 02 (March 13, 2017): 363–78. http://dx.doi.org/10.1142/s1793525317500182.

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We construct a sequence of balanced finite presentations of the trivial group with two generators and two relators with the following property: The minimal number of relations required to demonstrate that a generator represents the trivial element grows faster than the tower of exponentials of any fixed height of the length of the finite presentation.

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25

Dutta, S. P. "On modules of finite projective dimension." Nagoya Mathematical Journal 219 (September 2015): 87–111. http://dx.doi.org/10.1215/00277630-3140702.

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AbstractWe address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ring R of mixed characteristic p > 0, where p is a nonzero divisor, if I is an ideal of finite projective dimension over R and p 𝜖 I or p is a nonzero divisor on R/I, then every minimal generator of I is a nonzero divisor. Hence, if P is a prime ideal of finite projective dimension in a local ring R, then every minimal generator of P is a nonzero divisor in R.

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26

Srinivasulu, B., and Maheshanand Bhaintwal. "ℤ2(ℤ2 + uℤ2)-Additive cyclic codes and their duals." Discrete Mathematics, Algorithms and Applications 08, no. 02 (May 26, 2016): 1650027. http://dx.doi.org/10.1142/s1793830916500270.

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In this paper, we study some structural properties of [Formula: see text]-additive cyclic codes in [Formula: see text] as [Formula: see text]-submodules of [Formula: see text], where [Formula: see text]. The generators for these codes are obtained and a minimal spanning set is determined for even and odd [Formula: see text] separately with arbitrary [Formula: see text]. We also determine the generators of duals of the [Formula: see text]-additive cyclic codes for odd [Formula: see text]. A necessary condition for a 1-generator [Formula: see text]-cyclic code to be a [Formula: see text]-free module is obtained.

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27

Elias, Juan, Lorenzo Robbiano, and Giuseppe Valla. "Number of generators of ideals." Nagoya Mathematical Journal 123 (September 1991): 39–76. http://dx.doi.org/10.1017/s0027763000003640.

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Let I be a homogeneous ideal of a polynomial ring over a field, v(I) the number of elements of any minimal basis of I, e = e(I) the multiplicity or degree of R/I, h = h(I) the height or codimension of I, i = indeg (I) the initial degree of J, i.e. the minimal degree of non zero elements of I.This paper is mainly devoted to find bounds for v(I) when I ranges over large classes of ideals. For instance we get bounds when I ranges over the set of perfect ideals with preassigned codimension and multiplicity and when I ranges over the set of perfect ideals with preassigned codimension, multiplicity and initial degree. Moreover all the bounds are sharp since they are attained by suitable ideals. Now let us make some historical remarks.

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28

Yuhasz, George, and Erich Kaltofen. "Computing minimal generators of integer matrix sequences (abstract only)." ACM Communications in Computer Algebra 42, no. 1-2 (July 25, 2008): 91. http://dx.doi.org/10.1145/1394042.1394101.

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29

Gray, Robert D. "The minimal number of generators of a finite semigroup." Semigroup Forum 89, no. 1 (August 23, 2013): 135–54. http://dx.doi.org/10.1007/s00233-013-9521-8.

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30

Kostov, V. P. "The minimal number of generators of a matrix algebra." Journal of Dynamical and Control Systems 2, no. 4 (October 1996): 549–55. http://dx.doi.org/10.1007/bf02254702.

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31

Mezzetti, Emilia, and Rosa M. Miró-Roig. "The minimal number of generators of a Togliatti system." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 6 (February 12, 2016): 2077–98. http://dx.doi.org/10.1007/s10231-016-0554-y.

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32

Zhang, Pu, Ying-Bo Zhang, and Jin-Yun Guo. "Minimal Generators of Ringel–Hall Algebras of Affine Quivers." Journal of Algebra 239, no. 2 (May 2001): 675–704. http://dx.doi.org/10.1006/jabr.2000.8687.

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33

Oktaviani, Wiwin A., Taufik Barlian, and Yosi Apriani. "Studi Awal Karakteristik Tegangan Ouput Generator Magnet Permanen dan Generator DC pada Turbin Kubah Masjid Putar." Electrician 14, no. 2 (May 15, 2020): 56–63. http://dx.doi.org/10.23960/elc.v14n2.2149.

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Intisari — Setiap yang berputar memiliki potensi energi kinetik, tidak terkecuali putaran kubah masjid. Penelitian ini bertujuan untuk mengetahui potensi pemanfaatan kubah putar masjid sebagai penghasil energi listrik skala kecil. Generator yang diuji cobakan adalah generator magnet permanen dan generator DC yang dirangkaikan dengan turbin kubah putar. Pengujian dilakukan di dua lokasi, di Jembatan Musi 2 Palembang dan di perairan Sungsang Kabupaten Banyuasin untuk mengukur besaran tegangan dan arus output yang dihasilkan pada berbagai kecepatan angin menggunakan multimeter dan anemometer. Hasil penelitian menunjukkan bahwa tegangan yang dihasilkan oleh putaran kubah masjid menggunakan generator magnet permanen mampu mencapai 14,21 V pada kecepatan angin 3,8 m/det dibandingkan dengan generator DC yang hanya mencapai 3 V pada kecepatan angin 8 m/det. Jika ditinjau dari besaran arus, generator magnet permanen menghasilkan arus konstan sebesar 0,3 A sedangkan pada generator DC arus yang dihasilkan tidak terukur karena nilainya yang amat kecil. Penelitian ini menunjukkan bahwa kubah putar masjid dapat dijadikan sebagai turbin angin pada daerah yang memiliki kecepatan angin rendah. Kata kunci — kubah masjid putar,generator magnet permanen,generatorDC, turbin angin kecepatan rendah Abstract - Every spinning has kinetic energy potential; the mosque dome is no exception. This study aims to determine the potential use of the mosque's turning dome as a producer of small-scale electrical energy. Two types of the generator were tested, which were permanent magnet generator and DC generator, which were coupled with a rotary dome turbine. The test was carried out at two locations, at Palembang Musi 2 Bridge and in the waters of Sungsang, Banyuasin Regency, to measure the amount of voltage and output current generated at various wind speeds using a multimeter and anemometer. The results showed that the voltage generated by the mosque's dome rotation using a permanent magnet generator was able to reach 14.21 V at wind speeds of 3.8 m / sec compared to DC generators, which only reached 3 V at 8 m / s wind speed. When viewed from the amount of current, permanent magnet generators produce a constant current of 0.3 A while in DC generators, the current generated is not measurable because the value is minimal. This research shows that the mosque's rotary dome can be used as a wind turbine in areas that have low wind speeds. Keywords - rotary mosque domes, permanent magnet generators, generator DC, low speed wind turbines

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Tran, H. M., and H. Trinh. "Minimal-Order Functional Observer-Based Residual Generators for Fault Detection and Isolation of Dynamical Systems." Mathematical Problems in Engineering 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/2740645.

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This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.

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35

Jia, Boru, Andrew Smallbone, Rikard Mikalsen, K. V. Shivaprasad, Sumit Roy, and Anthony Paul Roskilly. "Performance Analysis of a Flexi-Fuel Turbine-Combined Free-Piston Engine Generator." Energies 12, no. 14 (July 11, 2019): 2657. http://dx.doi.org/10.3390/en12142657.

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The turbine-combined free-piston engine generator (TCFPEG) is a hybrid machine, generating both mechanical work from the gas turbine and electricity from the linear electric generator for battery charging. In the present study, the system performance of the designed TCFPEG system is predicted using a validated numerical model. A parametric analysis is undertaken based on the influence of the engine load, valve timing, the number of linear generators adopted, and different fuels on the system performance. It is found that when linear electric generators are connected with the free-piston gas turbine, the bottom dead centre, the peak piston velocity, and engine operation frequency are all reduced. Very minimal difference on the in-cylinder pressure and the compressor pressure is observed, while the peak pressure in the bounce chamber is reduced. When coupled with a linear electric generator, the system efficiency can be improved to nearly 50% by optimising engine load and the number of the linear generators adopted in the TCFPEG system. The system is able to be operated with different fuels as the piston is not limited by a mechanical system; the output power and system efficiency are highest when hydrogen is used as the fuel.

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36

Abramov, Y., V. Kryvtsova, and A. Mikhailyuk. "TECHNICAL CONDITION CONTROL ALGORITHM GAS GENERATORS OF STORAGE SYSTEMS AND HYDROGEN SUPPLY IN THE CONTEXT OF THEIR FIRE PREVENTION." Municipal economy of cities 1, no. 161 (March 26, 2021): 284–89. http://dx.doi.org/10.33042/2522-1809-2021-1-161-284-289.

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Algorithms for the control of the technical mill of gas generators in the systems of protection and supply of water, as an element of the systems of fire prevention. Algorithms for monitoring the dynamic parameters of gas generators of gas generators to control the flow and transmitting test signals to two types - from the viewer of the linearly growing function, or from the viewer of the straightforward view. One hundred percent before such test signals are broken down direct and indirect methods of control of the technical mill of gas generators in the systems of recovery and supply of water. It is shown that in the implementation of direct methods of control, no middle value of the parameters in the gas generators begins. To such parameters, the transmission efficiency is applied and continuously for an hour, as they characterize the dynamic power of gas generators in the systems of securing and supplying water. When implementing indirect methods of control, the integral characteristics of gas generators begin. In the quality of the information parameters, which are used to formulate the control algorithms, vibrating the vice in the empty gas generator of any average value. The values of these parameters are changed at two april given time of the hour, or at april given interval hour. In the quality of the criteria for the result of the control of the technical mill of the gas generators, the tolerance criteria are determined. It is shown that the priority in the vibration of the algorithm for the control of the technical mill of gas generators in the systems of gas generators and the supply of gas generators to the algorithm, which is based on the test signal in the form of a straight-flow gas generator. It should be considered that, when implementing such an algorithm, the control of the technical mill of gas generators in the systems of ensuring that the supply of vitality is kept to a minimum is minimal.

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37

KLIMENKO, ELENA, and NATALIA KOPTEVA. "ALL DISCRETE $\mathcal{RP}$ GROUPS WHOSE GENERATORS HAVE REAL TRACES." International Journal of Algebra and Computation 15, no. 03 (June 2005): 577–618. http://dx.doi.org/10.1142/s0218196705002438.

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In this paper we give necessary and sufficient conditions for discreteness of a subgroup of PSL(2,ℂ) generated by a hyperbolic element and an elliptic one of odd order with non-orthogonally intersecting axes. Thus we completely determine two-generator non-elementary Kleinian groups without invariant plane with real traces of the generators and their commutator. We also give a list of all parameters that correspond to such groups. An interesting corollary of the result is that the group of the minimal known volume hyperbolic orbifold ℍ3/Γ353 has real parameters.

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38

Jin, Cuicui, Weidong Li, Liu Liu, Ping Li, and Xian Wu. "A Coherency Identification Method of Active Frequency Response Control Based on Support Vector Clustering for Bulk Power System." Energies 12, no. 16 (August 16, 2019): 3155. http://dx.doi.org/10.3390/en12163155.

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Active frequency response (AFR) control is needed in current power systems. To solve the over-frequency problems of generators connected to non-disturbed buses during the AFR control period, the generators should be clustered into coherent groups. Thus, the control efficiency can be improved on the premise of ensuring control accuracy. Since the influencing factors (such as the model parameters, operation modes, and disturbance locations, etc.) of power system operation can be comprehensively reflected by the generator frequency, which is easily collected and calculated, the generator frequency can be used as the coherency identification input. In this paper, we propose a coherency identification method of AFR control based on support vector clustering for a bulk power system. By mapping data samples from the initial space to the high-dimensional feature space, the radius of the minimal enclosing sphere that can envelop all the data samples is obtained. Moreover, the coherency identification of generators is determined for AFR control according to the evaluating method of AFR clustering control effects and the evaluating index of cluster compactness and separation. The simulation results for the modified New England IEEE 10-generator 39-bus system and Henan power grid show that the proposed method is feasible and effective.

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39

Rant, William H. "Rings Whose Modules Require an Invariant Number of Minimal Generators." Missouri Journal of Mathematical Sciences 13, no. 1 (February 2001): 43–46. http://dx.doi.org/10.35834/2001/1301043.

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40

Benito-Picazo, F., P. Cordero, M. Enciso, and A. Mora. "Minimal generators, an affordable approach by means of massive computation." Journal of Supercomputing 75, no. 3 (June 4, 2018): 1350–67. http://dx.doi.org/10.1007/s11227-018-2453-z.

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41

González-Meneses, Juan, and Dolores Valladares. "On the centralizer of generic braids." Journal of Group Theory 21, no. 6 (November 1, 2018): 973–1000. http://dx.doi.org/10.1515/jgth-2018-0027.

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Abstract We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very particular structure. We present an algorithm to compute the centralizer of a braid whose generic-case complexity is quadratic on the length of the input, and which outputs a minimal set of generators in the generic case.

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42

Maharana, Manoj Kumar, and K. Shanti Swarup. "A Corrective Strategy to Alleviate Overloading in Transmission Lines Based on Particle Swarm Optimization Method." Journal of Engineering Research [TJER] 7, no. 1 (June 1, 2010): 31. http://dx.doi.org/10.24200/tjer.vol7iss1pp31-41.

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This paper presents novel corrective control actions to alleviate overloads in transmission lines by the Particle Swarm Optimization (PSO) method. Generator rescheduling and/or load shedding is performed locally, to restore the system from abnormal to normal operating state. The appropriate identification of generators and load buses to perform the corrective control action is an important task for the operators. Anew Direct Acyclic Graph (DAG) technique for selection of participating generators and buses with respect to a contingency is presented. The effectiveness of the proposed approach is demonstrated with the help of the IEEE 30 bus system. The result shows that the proposed approach is computationally fast, reliable and efficient, in restoring the system to normal state after a contingency with minimal control actions.

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43

Nersessian, A. "On the Geometry of Relativistic Anyon." Modern Physics Letters A 12, no. 24 (August 10, 1997): 1783–89. http://dx.doi.org/10.1142/s0217732397001813.

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A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators leads to the anyon model with free phase space which is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is described by irreducible representations of the (2+1)-dimensional Poincaré group.

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Rogers, Mark W., and Cameron Wickham. "Polynomials inducing the zero function on chain rings." Journal of Algebra and Its Applications 17, no. 08 (July 8, 2018): 1850160. http://dx.doi.org/10.1142/s0219498818501608.

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We provide a minimal set of generators for the ideal of polynomials in [Formula: see text] that map the maximal ideal [Formula: see text] into one of its powers [Formula: see text], where [Formula: see text] is a discrete valuation ring with a finite residue field. We use this to provide a minimal set of generators for the ideal of polynomials in [Formula: see text] that send [Formula: see text] to zero, where [Formula: see text] is a finite commutative local principal ideal ring.

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45

Cortadellas Benítez, Teresa, and Carlos D'Andrea. "Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with μ = 2." Canadian Journal of Mathematics 66, no. 6 (December 1, 2014): 1225–49. http://dx.doi.org/10.4153/cjm-2013-035-1.

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AbstractWe exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.

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46

Tang, Liming, and Wende Liu. "The minimal number of generators for finite-dimensional Cartan Lie superalgebras." Colloquium Mathematicum 158, no. 2 (2019): 305–12. http://dx.doi.org/10.4064/cm7628-11-2018.

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Normatov, Z. "On a minimal set of generators for Calogero-Moser space $C_4$." Uzbek Mathematical Journal 2019, no. 3 (September 17, 2019): 104–11. http://dx.doi.org/10.29229/uzmj.2019-3-12.

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Adamatzky, Andrew. "Nonconstructible blocks in 1D cellular automata: minimal generators and natural systems." Applied Mathematics and Computation 99, no. 1 (March 1999): 77–91. http://dx.doi.org/10.1016/s0096-3003(97)10177-1.

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Colarte, Liena, and Rosa M. Miró-Roig. "Minimal set of binomial generators for certain Veronese 3-fold projections." Journal of Pure and Applied Algebra 224, no. 2 (February 2020): 768–88. http://dx.doi.org/10.1016/j.jpaa.2019.06.009.

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Biteus, Jonas, and Mattias Nyberg. "Residual Generators for DAE Systems Utilizing Minimal Subsets of Model Equations." IFAC Proceedings Volumes 36, no. 5 (June 2003): 573–78. http://dx.doi.org/10.1016/s1474-6670(17)36553-9.

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Journal articles on the topic 'Minimal generators'

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