Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
-
Oswaldo Lezama
Abstract
We present the theory of Gröbner bases for the submodules of the free module 𝐴𝑚, 𝑚 ≥ 1, where 𝐴 = 𝑅[𝑥1,…,𝑥𝑛] and 𝑅 is a Noehterian commutative ring. This generalizes the theory of Gröbner bases for the ideals of 𝐴 and the submodules of (𝐾[𝑥1,…,𝑥𝑛])𝑚, where 𝐾 is a field, see [Möller, J. Symbolic Comput. 6: 345–359, 1988], [Möller, J. Algebra 100: 138–178, 1986] and [Zacharias, Generalized Gröbner bases in commutative polynomial rings, MIT, 1978]. This generalization to the submodules of 𝐴𝑚 was also partially considered in [Rutman, J. Symbolic Comput. 14: 483–503, 1992], however our presentation is more complete and detailed because we have included all algorithms, proofs and examples omitted in [Rutman, J. Symbolic Comput. 14: 483–503, 1992].
© Heldermann Verlag
Articles in the same Issue
- Functional Equations and μ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the 𝐿1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ω-Trees
- Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers
Articles in the same Issue
- Functional Equations and μ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the 𝐿1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ω-Trees
- Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers
