Conservation of the noetherianity by perfect transcendental field extensions

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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 $A\otimes_k k(t)_{per}$ 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 $k$.
14 pages, LaTeX (http://www.us.es/da/prepubli/nsprep8.pdf)

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Commutative Algebra, 13E05 (Primary) 13B35, 13A35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/61096

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0103099
 http://arxiv.org/abs/math/0103099

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arXiv