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Projective p-Orderings and Homogeneous Integer-Valued Polynomials

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Published/Copyright: August 4, 2011
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Integers
From the journal Volume 11 Issue 5

Abstract

Bhargava defined p-orderings of subsets of Dedekind domains and with them studied polynomials which take integer values on those subsets. In analogy with this construction for subsets of ℤ(p) and p-local integer-valued polynomials in one variable, we define projective p-orderings of subsets of . With such a projective p-ordering for we construct a basis for the module of homogeneous, p-local integer-valued polynomials in two variables.

Keywords.: p-Ordering; Homogeneous Polynomials; Integer-Valued Polynomials
Received: 2010-07-22
Accepted: 2011-01-16
Published Online: 2011-08-04
Published in Print: 2011-October

© de Gruyter 2011

Articles in the same Issue

  1. On Congruent Numbers with Three Prime Factors
  2. Projective p-Orderings and Homogeneous Integer-Valued Polynomials
  3. Analyzing Two-Color Babylon
  4. On the Number of Points in a Lattice Polytope
  5. Combinatorial Proofs of Some Identities for the Fibonacci and Lucas Numbers
  6. An Extreme Family of Generalized Frobenius Numbers
  7. On the Distance Between Smooth Numbers
  8. Analogs of the Stern Sequence
  9. On Some Equations Related to Ma's Conjecture
  10. Normality, Projective Normality and EGZ Theorem
  11. The (Exponential) Bipartitional Polynomials and Polynomial Sequences of Trinomial Type: Part II
  12. Supremum of Representation Functions
https://doi.org/10.1515/integ.2011.044
Keywords for this article
p-Ordering; Homogeneous Polynomials; Integer-Valued Polynomials

Articles in the same Issue

  1. On Congruent Numbers with Three Prime Factors
  2. Projective p-Orderings and Homogeneous Integer-Valued Polynomials
  3. Analyzing Two-Color Babylon
  4. On the Number of Points in a Lattice Polytope
  5. Combinatorial Proofs of Some Identities for the Fibonacci and Lucas Numbers
  6. An Extreme Family of Generalized Frobenius Numbers
  7. On the Distance Between Smooth Numbers
  8. Analogs of the Stern Sequence
  9. On Some Equations Related to Ma's Conjecture
  10. Normality, Projective Normality and EGZ Theorem
  11. The (Exponential) Bipartitional Polynomials and Polynomial Sequences of Trinomial Type: Part II
  12. Supremum of Representation Functions
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