With Two High Multiplication Of A_ ¡Þ - Algebra Structure

A special class of A_∞-algebras with two nontrivial higher multiplications, called (2, p, q)-algebras, are studied. Based on the construction theory of (2, p)-algebras, a method to construct a (2,p, g)-algebra from a general graded associative algebra is given, and meanwhile, some relations between (2,p, q)-algebras and (2,p)-algebras are discussed as well.