  In this paper we generalize to associative superalgebras Gerstenhaber's work
on cohomology structure of an associative algebra. We introduce two
multiplications U and [-,-] on the cochain complex C^*(A;A) of an associative
superalgebra A. We prove that these multiplications induce two multiplications
on H^*(A;A) and make it graded commutative superalgebra and graded Lie
superalgebra, respectively. Moreover, we introduce formal deformation theory of
associative superalgebras.
