Abstract:
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.
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