Author： Drensky Vesselin
Publisher： Taylor & Francis Ltd
ISSN： 0092-7872
Source： Communications in Algebra, Vol.39, Iss.4, 2011-04, pp. : 1344-1355
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Abstract
Let K be a field of any characteristic and let R be an algebra generated by two elements satisfying quadratic equations. Then R is a homomorphic image of F = K 〈x, y | x2 + ax + b = 0, y2 + cy + d = 0〉 for suitable a, b, c, d ∈ K. We establish that F can be embedded into the 2 × 2 matrix algebra [image omitted] with entries from the polynomial algebra [image omitted] over the algebraic closure of K and that F and [image omitted] satisfy the same polynomial identities as K-algebras. When the quadratic equations have double zeros, our result is a partial case of more general results by Ufnarovskij, Borisenko, and Belov from the 1980s. When each of the equations has different zeros, we improve a result of Weiss, also from the 1980s.
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