A while ago I worked on the question of what we can say if d^n=0, $d^n=0$, but I got distracted by more concrete problems. A few people have certainly thought about this question. One place to start looking is "$d\sp N=0$: $d^N=0$: generalized homology" or "Generalized homologies for $d\sp N=0$ d^N=0$and graded$q$-differential algebras" both by Michel Dubois-Violette. (Sorry for the lack of links; I'm off-campus so I can't actually get to the MathSciNet entries right now.) 1 A while ago I worked on the question of what we can say if d^n=0, but I got distracted by more concrete problems. A few people have certainly thought about this question. One place to start looking is "$d\sp N=0$: generalized homology" or "Generalized homologies for$d\sp N=0$and graded$q\$-differential algebras" both by Michel Dubois-Violette.