摘要

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 vertical bar x(2) + ax + b = 0, y(2) + cy + d = 0 > for suitable a, b, c, d. K. We establish that F can be embedded into the 2 x 2 matrix algebra M(2)((K) over bar [t]) with entries from the polynomial algebra (K) over bar [t] over the algebraic closure of K and that F and M(2)((K) over bar) satisfy the same polynomial identities as (K) over bar -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.

  • 出版日期2011