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Conservation of the noetherianity by perfect transcendental field extensions
2003
Revista matemática iberoamericana
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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 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