2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61096Let $k$ 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)Commutative Algebra13E05 (Primary) 13B35, 13A35 (Secondary)text