Generalized Lie Solvability of Associative Algebras

In this paper we consider generalized Lie algebra structures on graded associative algebras. We are interested in the situation where such structures are solvable and even commutative. We first prove some theorems in the case of solvable structures on semiprime, prime or simple associative algebras. Then we describe finite-dimensional associative algebras over an algebraically closed field of characteristic zero graded by a finite elementary abelian group which are generalized commutative under a skew-symmetric bicharacter on the grading group.