Associative Algebras Satisfying Quadratic Equations

This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X2 = aX + b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. The results obtained were validated computationally using the GAP system.