Abstract
Let D be a division algebra of finite dimension over any field K; we will consider left vector-spaces over D, whose dimension will always be assumed finite and > 0. If V and W are such spaces, we write Hom(V, W) for the space of homomorphisms of V into W, and let it operate on the right on V; in other words, if α is such a homomorphism, and v ∈ V, we write v α for the image of v under α. We consider Hom(V, W), in an obvious manner, as a vector-space over K; as such, it has a finite dimension, since it is a subspace of the space of K-linear mappings of V into W. As usual, we write End(V) for Hom(V, V).
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© 1967 Springer-Verlag Berlin · Heidelberg
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Weil, A. (1967). Simple algebras over local fields. In: Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00046-5_10
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DOI: https://doi.org/10.1007/978-3-662-00046-5_10
Publisher Name: Springer, Berlin, Heidelberg
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