Conservation of the noetherianity by perfect transcendental field extensions

Abstract

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)