Cohomological triviality of bimodules over Frobenius algebras

The structure of Frobenius $Z_p$-algebras with disjointness condition is studied. When $p=2$ an analogue of Nakayama's theorem on cohomological triviality is proved for suitable algebras whose radical squared is zero. When $p\ne2$, cohomological triviality in all dimensions will not generally be implied by the vanishing of cohomology in a single dimension, but will follow from the vanishing in two successive dimensions.
Bibliography: 9 titles.