Titlebook: Basic Number Theory; André Weil Book 1995Latest edition Springer-Verlag Berlin Heidelberg 1995 algebraic number field.algebraic number the

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Simple algebrasnd carrying no additional structure. All fields are understood to be commutative. All algebras are understood to have a unit, to be of finite dimension over their ground-field, and to be central over that field (an algebra . over . is called central if . is its center). If ., . are algebras over . w

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Simple algebras over local fieldsinite and > 0. If . and . are such spaces, we write Hom(., .) for the space of homomorphisms of . into ., and let it operate on the right on .; in other words, if . is such a homomorphism, and . ∈ ., we write . for the image of . under .. We consider Hom(., .), in an obvious manner, as a vector-spac

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Simple algebras over A-fieldscipally concerned with a simple algebra . over .; as stipulated in Chapter IX, it is always understood that . is central, i. e. that its center is ., and that it has a finite dimension over .; by corollary 3 of prop. 3, Chap. IX-1, this dimension can then be written as ., where . is an integer ≥ 1.

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https://doi.org/10.1007/978-3-642-77247-4ates, one sees that all linear mappings of such spaces into one another are continuous; in particular, linear forms are continuous. Similarly, every injective linear mapping of such a space . into another is an isomorphism of . onto its image. As . is not compact, no subspace of . can be compact, except {0}.

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0072-7830 y in 1961-62; at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript b

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Anita F. Meier,Andrea S. Laimbacherdimension ., and the number of its elements is . = .. If . is a subfield of a field . with . = . elements, . may also be regarded e.g. as a left vector-space over .; if its dimension as such is ., we have . = . and . = . = ..

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