92
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Effective Genericity, δ-Regularity and Strong Noether Position

Pages 3933-3949 | Received 06 Sep 2010, Accepted 11 Jun 2011, Published online: 11 Sep 2012

REFERENCES

  • Bayer , D. , Stillman , M. ( 1987 ). A criterion for detecting m-regularity . Invent. Math. 87 : 1 – 11 .
  • Bermejo , I. , Gimenez , P. ( 2006 ). Saturation and Castelnuovo-Mumford regularity . J. Alg. 303 : 592 – 617 .
  • Caviglia , G. , Sbarra , E. ( 2005 ). Characteristic-free bounds for the Castelnuovo-Mumford regularity . Compos. Math. 141 : 1365 – 1373 .
  • Decker , W. , Greuel , G. M. , Pfister , G. ( 1999 ). Primary decomposition: Algorithms and comparisons . In: Matzat , B. H. , Greuel , G. M. , Hiss , G. , eds. Algorithmic Algebra and Number Theory . Heidelberg : Springer-Verlag , pp. 187 – 220 .
  • Eisenbud , D. , Goto , S. ( 1984 ). Linear free resolutions and minimal multiplicity . J. Alg. 88 : 89 – 133 .
  • Eisenbud , D. , Sturmfels , B. ( 1994 ). Finding sparse systems of parameters . J. Pure Appl. Alg. 94 : 143 – 157 .
  • Gerdt , V. P. ( 2000 ). On the relation between Pommaret and Janet bases . In: Ghanza , V. G. , Mayr , E. W. , Vorozhtsov , E. V. , eds. Computer Algebra in Scientific Computing—CASC 2000 . Berlin : Springer-Verlag , pp. 167 – 182 .
  • Gerdt , V. P. , Blinkov , Yu. A. ( 1998 ). Involutive bases of polynomial ideals . Math. Comp. Simul. 45 : 519 – 542 .
  • Gerdt , V. P. , Blinkov , Yu. A. ( 1998 ). Minimal involutive bases . Math. Comp. Simul. 45 : 543 – 560 .
  • Guillemin , V. W. , Sternberg , S. (1964). An algebraic model of transitive differential geometry. Bull. Amer. Math. Soc. 70:16–47 (With a letter of Serre as appendix).
  • Hashemi , A. ( 2010 ). Strong Noether position and stabilized regularities . Comm. Alg. 38 : 515 – 533 .
  • Hausdorf , M. , Sahbi , M. , Seiler , W. M. ( 2006 ). δ- and quasi-regularity for polynomial ideals . In: Calmet , J. , Seiler , W. M. , Tucker , R. W. , eds. Global Integrability of Field Theories . Karlsruhe : Universitätsverlag Karlsruhe , pp. 179 – 200 .
  • Hausdorf , M. , Seiler , W. M. ( 2002 ). An efficient algebraic algorithm for the geometric completion to involution . Appl. Alg. Eng. Comm. Comp. 13 : 163 – 207 .
  • Herzog , J. , Popescu , D. , Vladoiu , M. ( 2003 ). On the Ext-Modules of Ideals of Borel Type . Commutative Algebra, Contemp. Math. 331 . Providence , RI : Amer. Math. Soc. , pp. 171 – 186 .
  • Mall , D. ( 1998 ). On the relation between Gröbner and Pommaret bases . Appl. Alg. Eng. Comm. Comp. 9 : 117 – 123 .
  • Robertz , D. ( 2009 ). Noether normalization guided by monomial cone decompositions . J. Symb. Comp. 44 : 1359 – 1373 .
  • Schenzel , P. , Trung , N. V. , Cuong , N. T. ( 1978 ). Verallgemeinerte Cohen–Macaulay–Moduln . Math. Nachr. 85 : 57 – 73 .
  • Schreyer , F. O. ( 1980 ). Die Berechnung von Syzygien mit dem verallgemeinerten Weierstraßschen Divisionssatz. Master's thesis, Fakultät für Mathematik, Universität Hamburg .
  • Seiler , W. M. ( 1994 ). On the arbitrariness of the general solution of an involutive partial differential equation . J. Math. Phys. 35 : 486 – 498 .
  • Seiler , W. M. ( 2007 ). Spencer cohomology, differential equations, and Pommaret bases . In: Rosenkranz , M. , Wang , D. , eds. Gröbner Bases in Symbolic Analysis . Radon Series on Computation and Applied Mathematics 2 . Berlin : Walter de Gruyter , pp. 171 – 219 .
  • Seiler , W. M. ( 2009 ). A combinatorial approach to involution and δ-regularity I: Involutive bases in polynomial algebras of solvable type . Appl. Alg. Eng. Comm. Comp. 20 : 207 – 259 .
  • Seiler , W. M. ( 2009 ). A combinatorial approach to involution and δ-regularity II: Structure analysis of polynomial modules with Pommaret bases . Appl. Alg. Eng. Comm. Comp. 20 : 261 – 338 .
  • Seiler , W. M. ( 2010 ). Involution—The Formal Theory of Differential Equations and Its Applications in Computer Algebra . Algorithms and Computation in Mathematics 24 . Berlin : Springer-Verlag .
  • Communicated by I. Swanson.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.