  In this article, we introduce two multiplications U and [-;-] on the cochain
complex C*(A;A) of an associative superalgebra A such that C*(A;A) is a
differential graded Lie superalgebra and a differential graded associative
superalgebra with respect to [-;-] and U, respectively. We prove that these
multiplications induce two multiplications U and [-;-] on the cohomology
H*(A;A) of A such that H*(A;A) is a Z-graded Lie superalgebra with respect to
[-;-] and a Z-graded commutative superalgebra with respect to U. Also, we prove
that if P is a two sided module over an associative superalgebra A, then H*(A;
P) is a two sided module over H*(A;A).
