"... the theory of valuations may be viewed as a branch of topological algebra. In fact, historically speaking, it represents the first invasion of topology, more precisely, of early metric topology, into the domains of algebra. The introduction of metric methods into algebra has been so fruitful that today many of the deeper algebraic theories carry their mark. In this regard, one should distinguish between the classical use in algebra of the natural metric of the real or complex number fields, such as in proving the "fundamental theorem of algebra," and the much more recent use of the far less evident metrics which are derived from arithmetic notions of divisibility and which constitute the principal notion of valuation theory. Such a metric occurs for the first time in Hensel's construction of the p-adic numbers ..."
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Academics from the United StatesJews from the United StatesMathematicians from the United StatesMathematicians from GermanyJews from Germany
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Gerhard Hochschild
Gerhard Paul Hochschild (April 29, 1915 – July 8, 2010) was a German-born American mathematician, who did research on Lie groups, algebraic groups, homological algebra and algebraic number theory. He is known for Hochschild homology. In 1979 he was elected to United States National Academy of Sciences.
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