Conservation of the noetherianity by perfect transcendental field extensions
Copyright policy )Conservation of the noetherianity by perfect transcendental field extensions
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}=\bigcup_{m\geq 0}(A\otimes_k k(t^{\frac{1}{p^m}})) 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 .
- Universidad de Sevilla (US) Spain
- University of Seville Spain
perfect closure, 13E05 (Primary) 13B35, 13A35 (Secondary), noetherian ring, algebra of power series, Perfect-power series ring, 13E05, Commutative Algebra (math.AC), Noetherian ring, power series ring, FOS: Mathematics, 13A35, complete local ring, 13B35, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Completion of commutative rings, positive characteristic, perfect field, Mathematics - Commutative Algebra, Algebraic field extensions, Complete local ring, Perfect extension, Noetherianity of tensor product, algebraic extension, Commutative Noetherian rings and modules
perfect closure, 13E05 (Primary) 13B35, 13A35 (Secondary), noetherian ring, algebra of power series, Perfect-power series ring, 13E05, Commutative Algebra (math.AC), Noetherian ring, power series ring, FOS: Mathematics, 13A35, complete local ring, 13B35, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Completion of commutative rings, positive characteristic, perfect field, Mathematics - Commutative Algebra, Algebraic field extensions, Complete local ring, Perfect extension, Noetherianity of tensor product, algebraic extension, Commutative Noetherian rings and modules
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