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Binomial vanishing ideals

Year 2015, Volume: 2 Issue: 2, 151 - 156, 30.04.2015

Azucena Tochimani Rafael H. Villarreal

https://doi.org/10.13069/jacodesmath.12847
Cited By: 1

Abstract

In this note we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.

Keywords

Vanishing ideal Binomial ideal Monomial parameterization Projective variety

References

  • D. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms, Springer-Verlag, 1992.
  • D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J., 84(1), 1-45, 1996.
  • M. Gasca and T. Sauer, Polynomial interpolation in several variables, Adv. Comput. Math., 12(4), 377-410, 2000.
  • M. González-Sarabia, C. Rentería and H. Tapia-Recillas, Reed-Muller-type codes over the Segre va- riety, Finite Fields Appl., 8(4), 511-518, 2002.
  • J. Harris, Algebraic geometry: A first course, Graduate Texts in Mathematics 133, Springer-Verlag, New York, 1992.
  • M. Hellus and R. Waldi, Interpolation in affine and projective space over a finite field, J. Commut. Algebra, to appear. N. Jacobson, Basic algebra I , Second Edition, W. H. Freeman and Company, New York, 1996.
  • H. H. López, C. Rentería and R. H. Villarreal, Affine cartesian codes, Des. Codes Cryptogr., 71(1), 5-19, 2014.
  • J. Neves, M. Vaz Pinto and R. H. Villarreal, Regularity and algebraic properties of certain lattice ideals, Bull. Braz. Math. Soc. (N.S.), 45(4), 777-806, 2014.
  • L. O’Carroll, F. Planas-Vilanova and R. H. Villarreal, Degree and algebraic properties of lattice and matrix ideals, SIAM J. Discrete Math., 28(1), 394-427, 2014.
  • A. Tochimani and R. H. Villarreal, Vanishing ideals over rational parameterizations, preprint, arXiv:1502.05451v1, 2015.
  • R. H. Villarreal, Monomial algebras, second edition, Monographs and Research Notes in Mathematics, CRC Press, 2015.

Binomial vanishing ideals

Year 2015, Volume: 2 Issue: 2, 151 - 156, 30.04.2015

Azucena Tochimani Rafael H. Villarreal

https://doi.org/10.13069/jacodesmath.12847
Cited By: 1

Abstract

References

  • D. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms, Springer-Verlag, 1992.
  • D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J., 84(1), 1-45, 1996.
  • M. Gasca and T. Sauer, Polynomial interpolation in several variables, Adv. Comput. Math., 12(4), 377-410, 2000.
  • M. González-Sarabia, C. Rentería and H. Tapia-Recillas, Reed-Muller-type codes over the Segre va- riety, Finite Fields Appl., 8(4), 511-518, 2002.
  • J. Harris, Algebraic geometry: A first course, Graduate Texts in Mathematics 133, Springer-Verlag, New York, 1992.
  • M. Hellus and R. Waldi, Interpolation in affine and projective space over a finite field, J. Commut. Algebra, to appear. N. Jacobson, Basic algebra I , Second Edition, W. H. Freeman and Company, New York, 1996.
  • H. H. López, C. Rentería and R. H. Villarreal, Affine cartesian codes, Des. Codes Cryptogr., 71(1), 5-19, 2014.
  • J. Neves, M. Vaz Pinto and R. H. Villarreal, Regularity and algebraic properties of certain lattice ideals, Bull. Braz. Math. Soc. (N.S.), 45(4), 777-806, 2014.
  • L. O’Carroll, F. Planas-Vilanova and R. H. Villarreal, Degree and algebraic properties of lattice and matrix ideals, SIAM J. Discrete Math., 28(1), 394-427, 2014.
  • A. Tochimani and R. H. Villarreal, Vanishing ideals over rational parameterizations, preprint, arXiv:1502.05451v1, 2015.
  • R. H. Villarreal, Monomial algebras, second edition, Monographs and Research Notes in Mathematics, CRC Press, 2015.
There are 11 citations in total.

Details

Primary Language English
Authors

Azucena Tochimani This is me

Rafael H. Villarreal This is me

Publication Date April 30, 2015
Published in Issue Year 2015 Volume: 2 Issue: 2

Cite

APA Tochimani, A., & Villarreal, R. H. (2015). Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications, 2(2), 151-156. https://doi.org/10.13069/jacodesmath.12847
AMA Tochimani A, Villarreal RH. Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications. April 2015;2(2):151-156. doi:10.13069/jacodesmath.12847
Chicago Tochimani, Azucena, and Rafael H. Villarreal. “Binomial Vanishing Ideals”. Journal of Algebra Combinatorics Discrete Structures and Applications 2, no. 2 (April 2015): 151-56. https://doi.org/10.13069/jacodesmath.12847.
EndNote Tochimani A, Villarreal RH (April 1, 2015) Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications 2 2 151–156.
IEEE A. Tochimani and R. H. Villarreal, “Binomial vanishing ideals”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 2, no. 2, pp. 151–156, 2015, doi: 10.13069/jacodesmath.12847.
ISNAD Tochimani, Azucena - Villarreal, Rafael H. “Binomial Vanishing Ideals”. Journal of Algebra Combinatorics Discrete Structures and Applications 2/2 (April2015), 151-156. https://doi.org/10.13069/jacodesmath.12847.
JAMA Tochimani A, Villarreal RH. Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2:151–156.
MLA Tochimani, Azucena and Rafael H. Villarreal. “Binomial Vanishing Ideals”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 2, no. 2, 2015, pp. 151-6, doi:10.13069/jacodesmath.12847.
Vancouver Tochimani A, Villarreal RH. Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2(2):151-6.

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