Conservation of the noetherianity by perfect transcendental field extensions

Details Conservation of the noetherianity by perfect transcendental field extensions Conservation of the noetherianity by perfect transcendental field extensions

2001-03-15

arxiv.org/abs/math/0103099v1

Mathematics

Commutative Algebra

14 pages, LaTeX (http://www.us.es/da/prepubli/nsprep8.pdf)

Scientific paper

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 $k$.

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