Conservation of the noetherianity by perfect transcendental field extensions

Magdalena Fernández Lebrón, Luis Narváez Macarro
2003 Revista matemática iberoamericana  
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 is noetherian or not. As a consequence, we prove that the ring A ⊗ k k(t) per is noetherian when A is the ring of formal power series in n indeterminates over k. 2000 Mathematics Subject Classification: 13E05, 13B35, 13A35.
doi:10.4171/rmi/351 fatcat:o5n3dtcaa5ghddjhdzskjptqrm