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September, 2003 Conservation of the noetherianity by perfect transcendental field extensions
Magdalena Fernández-Lebrón, Luis Narváez
Rev. Mat. Iberoamericana 19(2): 355-366 (September, 2003).


Let $k$ be a perfect field of characteristic $p>0$, $k(t)_{per}$ the perfect closure of $k(t)$ and $A$ a $k$-algebra. We characterize whether the ring $$ A\otimes_k k(t)_{per}=\bigcup_{m\geq 0}(A\otimes_k k(t^{\frac{1}{p^m}})) $$ is noetherian or not. As a consequence, we prove that the ring $A\otimes_k k(t)_{per}$ is noetherian when $A$ is the ring of formal power series in $n$ indeterminates over $k$.


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Magdalena Fernández-Lebrón. Luis Narváez. "Conservation of the noetherianity by perfect transcendental field extensions." Rev. Mat. Iberoamericana 19 (2) 355 - 366, September, 2003.


Published: September, 2003
First available in Project Euclid: 8 September 2003

zbMATH: 1084.13502
MathSciNet: MR2023189

Primary: 13A35 , 13B35 , 13E05

Keywords: complete local ring , Noetherian ring , perfect closure , perfect field , power series ring

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 2 • September, 2003
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