Some properties of the symbol algebras
نویسندگان
چکیده
algebra. First, we recall some definitions in the theory of associative algebras. LetA 6= 0 be an algebra over the fieldK. If the equations ax = b, ya = b, ∀a, b ∈ A, a 6= 0, have unique solutions, then the algebra A is called a division algebra. If A is a finite-dimensional algebra, then A is a division algebra if and only if A is without zero divisors (x 6= 0, y 6= 0 ⇒ xy 6= 0).(see [9]) Let K be a field with charK 6= 2. Let HK (α, β) be a quaternion algebra with basis {1, e1, e2, e3} and the multiplication given by
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