@Article{         10.2307/24492715,
  Author        = "SOC{\'I}AS, GUILLERMO MORENO",
  Abstract      = "In a polynomial ring K[X1,..., Xn] over a field, let I0 ⊂ I1 ⊂ ··· ⊂ Is be a strictly ascending chain of ideals, with the contition that every Ii can be generated by elements of degree not greater than f(i). A. Seidenberg showed that there is a bound on the length s of such a chain depending only on n and f, which is recursive in f for every n and primitive recursive in f for n = 2. In this paper we give a better bound, expressed in a rather simple way in terms of f, which is attained when f is an increasing function. We prove that it is primitive recursive in f for all n. We also show that, on the contrary, there is no bound which is primitive recursive in n in general.",
  date-added    = "2021-10-08 12:59:49 +0200",
  date-modified = "2021-10-08 12:59:49 +0200",
  ISSN          = "00255521, 19031807",
  Journal       = "Mathematica Scandinavica",
  Number        = "2",
  Pages         = "181--205",
  Publisher     = "Mathematica Scandinavica",
  Title         = "LENGTH OF POLYNOMIAL ASCENDING CHAINS AND PRIMITIVE RECURSIVENESS",
  URL           = "http://www.jstor.org/stable/24492715",
  Volume        = "71",
  Year          = "1992",
  bdsk-url-1    = "http://www.jstor.org/stable/24492715",
  File          = "LENGTH OF POLYNOMIAL ASCENDING CHAINS AND PRIMITIVE RECURSIVENESS - 24492715.pdf"
}

@Article{ 10.2307/24492715, Author = "SOC{\'I}AS, GUILLERMO MORENO", Abstract = "In a polynomial ring K[X1,..., Xn] over a field, let I0 ⊂ I1 ⊂ ··· ⊂ Is be a strictly ascending chain of ideals, with the contition that every Ii can be generated by elements of degree not greater than f(i). A. Seidenberg showed that there is a bound on the length s of such a chain depending only on n and f, which is recursive in f for every n and primitive recursive in f for n = 2. In this paper we give a better bound, expressed in a rather simple way in terms of f, which is attained when f is an increasing function. We prove that it is primitive recursive in f for all n. We also show that, on the contrary, there is no bound which is primitive recursive in n in general.", date-added = "2021-10-08 12:59:49 +0200", date-modified = "2021-10-08 12:59:49 +0200", ISSN = "00255521, 19031807", Journal = "Mathematica Scandinavica", Number = "2", Pages = "181--205", Publisher = "Mathematica Scandinavica", Title = "LENGTH OF POLYNOMIAL ASCENDING CHAINS AND PRIMITIVE RECURSIVENESS", URL = "http://www.jstor.org/stable/24492715", Volume = "71", Year = "1992", bdsk-url-1 = "http://www.jstor.org/stable/24492715", File = "LENGTH OF POLYNOMIAL ASCENDING CHAINS AND PRIMITIVE RECURSIVENESS - 24492715.pdf" }