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Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras

  • Huishi Li EMAIL logo
Published/Copyright: February 21, 2017
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 25 Issue 3

Abstract

Let K⁢〈X〉=K⁢〈X1,…,Xn〉 be the free algebra generated by X={X1,…,Xn} over a field K. It is shown that, with respect to any weighted ℕ-gradation attached to K⁢〈X〉, minimal homogeneous generating sets for finitely generated graded two-sided ideals of K⁢〈X〉 can be algorithmically computed, and that if an ungraded two-sided ideal I of K⁢〈X〉 has a finite Gröbner basis 𝒢 with respect to a graded monomial ordering on K⁢〈X〉, then a minimal standard basis for I can be computed via computing a minimal homogeneous generating set of the associated graded ideal 〈𝐋𝐇⁢(I)〉.

Keywords: Free algebra; homogeneous generating set; Gröbner basis; standard basis
MSC 2010: 16W70; 16Z05

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Received: 2014-11-03
Accepted: 2016-04-01
Published Online: 2017-02-21
Published in Print: 2018-09-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Semilinear fractional order integro-differential inclusions with infinite delay
  3. Quasi-nilpotent perturbations of the generalized Kato spectrum
  4. Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
  5. Relations between BV*(q;α) and Λ*BVp classes of functions
  6. On the constancy of signs and order of magnitude of Fourier–Haar coefficients
  7. On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations
  8. Optimal control problem for the equation of vibrations of an elastic plate
  9. Generalized Hausdorff capacities and their applications
  10. Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
  11. A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field
  12. A note on the Borel types of some small sets
  13. On some boundary value problems for the heat equation in a non-regular type of a prism of ℝN+1
  14. Some weighted integral inequalities for differentiable h-preinvex functions
  15. Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
  16. On Baer invariants of pairs of groups
  17. The Arzelà–Ascoli theorem by means of ideal convergence
  18. Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV
https://doi.org/10.1515/gmj-2017-0006
Keywords for this article
Free algebra; homogeneous generating set; Gröbner basis; standard basis

Articles in the same Issue

  1. Frontmatter
  2. Semilinear fractional order integro-differential inclusions with infinite delay
  3. Quasi-nilpotent perturbations of the generalized Kato spectrum
  4. Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
  5. Relations between BV*(q;α) and Λ*BVp classes of functions
  6. On the constancy of signs and order of magnitude of Fourier–Haar coefficients
  7. On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations
  8. Optimal control problem for the equation of vibrations of an elastic plate
  9. Generalized Hausdorff capacities and their applications
  10. Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
  11. A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field
  12. A note on the Borel types of some small sets
  13. On some boundary value problems for the heat equation in a non-regular type of a prism of ℝN+1
  14. Some weighted integral inequalities for differentiable h-preinvex functions
  15. Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
  16. On Baer invariants of pairs of groups
  17. The Arzelà–Ascoli theorem by means of ideal convergence
  18. Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV
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