The following result is proved: Let B be a block ideal of group algebr
a kG over a splitting field k with characteristic p. Suppose that B ha
s only one irreducible module L and abelian defect group D, then B con
gruent-to Mat(m)(kD), where m = Dim(k) L. This result generalizes Kuls
hammer's theorem concerning the structure of block algebras with inert
ial index 1.