BibTex RIS Kaynak Göster

Binomial vanishing ideals

Yıl 2015, Cilt: 2 Sayı: 2, 151 - 156, 30.04.2015

Azucena Tochimani Rafael H. Villarreal

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

Öz

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

Anahtar Kelimeler

Vanishing ideal Binomial ideal Monomial parameterization Projective variety

Kaynakça

  • 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

Yıl 2015, Cilt: 2 Sayı: 2, 151 - 156, 30.04.2015

Azucena Tochimani Rafael H. Villarreal

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

Öz

Kaynakça

  • 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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Yazarlar

Azucena Tochimani Bu kişi benim

Rafael H. Villarreal Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 2 Sayı: 2

Kaynak Göster

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. Nisan 2015;2(2):151-156. doi:10.13069/jacodesmath.12847
Chicago Tochimani, Azucena, ve Rafael H. Villarreal. “Binomial vanishing ideals”. Journal of Algebra Combinatorics Discrete Structures and Applications 2, sy. 2 (Nisan 2015): 151-56. https://doi.org/10.13069/jacodesmath.12847.
EndNote Tochimani A, Villarreal RH (01 Nisan 2015) Binomial vanishing ideals. Journal of Algebra Combinatorics Discrete Structures and Applications 2 2 151–156.
IEEE A. Tochimani ve R. H. Villarreal, “Binomial vanishing ideals”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 2, ss. 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 (Nisan2015), 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 ve Rafael H. Villarreal. “Binomial vanishing ideals”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 2, 2015, ss. 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.

Cited By

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Azucena Tochimani
https://doi.org/10.1007/s40840-015-0239-5