JournalsrmiVol. 19, No. 2pp. 355–366

Conservation of the noetherianity by perfect transcendental field extensions

  • Magdalena Fernández Lebrón

    Universidad de Sevilla, Spain
  • Luis Narváez Macarro

    Universidad de Sevilla, Spain
Conservation of the noetherianity by perfect transcendental field extensions cover
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Abstract

Let kk be a perfect field of characteristic p>0p>0, k(t)perk(t)_{per} the perfect closure of k(t)k(t) and AA a kk-algebra. We characterize whether the ring

Akk(t)per=m0(Akk(t1pm))A\otimes_k k(t)_{per}=\bigcup_{m\geq 0}(A\otimes_k k(t^{\frac{1}{p^m}}))

is noetherian or not. As a consequence, we prove that the ring Akk(t)perA\otimes_k k(t)_{per} is noetherian when AA is the ring of formal power series in nn indeterminates over kk.

Cite this article

Magdalena Fernández Lebrón, Luis Narváez Macarro, Conservation of the noetherianity by perfect transcendental field extensions. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 355–366

DOI 10.4171/RMI/351