Abstract
18.1. Let us first recall the notion of an algebra over a field that we introduced in §11.1. By an algebra over a field F, or simply by an F -algebra, we understand an associative ring A which is also a vector space over F such that \((ax)(by)=abxy\) for \(\,a,\,b\in F\) and \(\,x,\,y\in A.\) If A has an identity element, we denote it by \(1_A,\) or simply by \(1.\) Identifying \(\,a\,\) with \(\,a1_A\) for every \(\,a\in F,\) we can view F as a subring of A.
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Shimura, G. (2010). Algebras Over a Field. In: Arithmetic of Quadratic Forms. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1732-4_4
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DOI: https://doi.org/10.1007/978-1-4419-1732-4_4
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