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3 results

  • The Pierce-Birkhoff Conjecture for Curves

  • Murray Marshall
  • Journal:
    Canadian Journal of Mathematics / Volume 44 / Issue 6 / 01 December 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 1262-1271
    Print publication:
    01 December 1992
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  • The results obtained extend Madden’s result for Dedekind domains to more general types of 1-dimensional Noetherian rings. In particular, these results apply to piecewise polynomial functions t:C → R where R is a real closed field and C ⊆ Rn is a closed 1-dimensional semi-algebraic set, and also to the associated “relative” case where t, C are defined over some subfield K ⊆ R.

  • A Note on the Dubois-Efroymson Dimension Theorem

  • Wojciech Kucharz
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 1 / 01 March 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 24-29
    Print publication:
    01 March 1989
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  • Let X ⊂ Rnn be an irreducible nonsingular algebraic set and let Z be an algebraic subset of X with dim Z ≦ dim X — 2. In this paper it is shown that there exists an irreducible algebraic subset Y of X satisfying the following conditions: dim Y = dim X — 1, Z ⊂ Y and that the ideal of regular functions on X vanishing on Y is principal.

  • On Complete Intersections Over an Algebraically Non-Closed Field

  • Maria Grazia Marinari, Mario Raimondo
  • Journal:
    Canadian Mathematical Bulletin / Volume 29 / Issue 2 / 01 June 1986
    Published online by Cambridge University Press:
    20 November 2018, pp. 140-145
    Print publication:
    01 June 1986
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  • We give a criterion in order that an affine variety defined over any field has a complete intersection (ci.) embedding into some affine space. Moreover we give an example of a smooth real curve C all of whose embeddings into affine spaces are c.i.; nevertheless it has an embedding into ℝ3 which cannot be realized as a c.i. by polynomials.