Associative Algebras Satisfying Quadratic Equations
Josimar da Silva Rocha *
Department of Mathematics, Federal University of Technology-Paran´a, Av. Alberto Carazzai, 1640, Corn´elio Proc´opio, Paran´a, 86300-000, Brazil.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Associative algebra, Polynomial identity, Nilpotency index, Nagata-Higman Theorem