  The objective of this paper is to develop diassociative analogues of
Lie-theoretic results from Peggy Batten's 1993 dissertation. We first prove
that covers of diassociative algebras are unique. Second, we show that the
multiplier of a diassociative algebra is characterized by the second cohomology
group with coefficients in the field. Third, we establish criteria for when the
center of a cover maps onto the center of the algebra. Along the way, we obtain
a collection of exact sequences, characterizations, and a brief theory of
unicentral diassociative algebras and stem extensions. This paper is part of an
ongoing project to advance extension theory in the context of several Loday
algebras.
