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Approval of AI-Based Medical Devices in China From 2020 to 2025: Retrospective Analysis.
JMIR Med InformZhang L, Yan J.
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The Annals of Mathematics, 1950
Local class field theory is treated by means of cohomology theory. Let \(L/K\) be a Galois extension with Galois group \(\mathfrak L\). Let \(\mathfrak H\) be an invariant subgroup of \(\mathfrak L\), and \(F\) be the corresponding subfield of \(L\). The lifting \(\lambda\) of the Galois 2-cohomology group \(H^2(\mathfrak L/\mathfrak H, F^*)\) \((F^*\)
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Local class field theory is treated by means of cohomology theory. Let \(L/K\) be a Galois extension with Galois group \(\mathfrak L\). Let \(\mathfrak H\) be an invariant subgroup of \(\mathfrak L\), and \(F\) be the corresponding subfield of \(L\). The lifting \(\lambda\) of the Galois 2-cohomology group \(H^2(\mathfrak L/\mathfrak H, F^*)\) \((F^*\)
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1988
Let k be a finite field with q = pn elements and let V be an algebraic variety defined over k (or, as one also says, a k-variety). Suppose that V is defined by charts Ui (isomorphic to affine k-varieties) and changes of coordinates uij (with coefficients in k).
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Let k be a finite field with q = pn elements and let V be an algebraic variety defined over k (or, as one also says, a k-variety). Suppose that V is defined by charts Ui (isomorphic to affine k-varieties) and changes of coordinates uij (with coefficients in k).
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2003
Global class field theory is a major achievement of algebraic number theory, based on the Artin reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's ...
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Global class field theory is a major achievement of algebraic number theory, based on the Artin reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's ...
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1997
There are two main problems in the theory of algebraic number fields: On the one hand the description of the arithmetical properties of a given number field and on the other hand the description of number fields with given arithmetical properties.
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There are two main problems in the theory of algebraic number fields: On the one hand the description of the arithmetical properties of a given number field and on the other hand the description of number fields with given arithmetical properties.
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Class Field Theory. Field Extensions
1971In this brief survey on class field theory and related questions we mainly present the papers reviewed in the “Mathematics” section of Referativnyi Zhurnal during 1958–1967. Among the books published during this time we note those by Chevalley [20] (a systematic exposition and application of cohomology groups), Artin and Tate [12] (the most modern ...
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1986
The abstract class field theory that we have developed in the last chapter is now going to be applied to the case of a local field, i.e., to a field which is complete with respect to a discrete valuation, and which has a finite residue class field. By chap. II, (5.2), these are precisely the finite extensions K of the fields ℚ p or F p ((t)).
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The abstract class field theory that we have developed in the last chapter is now going to be applied to the case of a local field, i.e., to a field which is complete with respect to a discrete valuation, and which has a finite residue class field. By chap. II, (5.2), these are precisely the finite extensions K of the fields ℚ p or F p ((t)).
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