On Superderivations and Jordan Superderivations of Incidence Superalgebras

In this paper we study superderivations and Jordan superderivations of incidence superalgebras of locally finite Z2-graded posets. We prove that every superderivation can be expressed as a sum of an inner superderivation, an additive superderivation, and a ring superderivation; if the coefficient ring has inner derivations only, then every superderivation is inner. We also show that every Jordan superderivation decomposes uniquely as a sum of a superderivation and a proper Jordan superderivation that vanishes on the even part. These results extend classical results on incidence algebras to the supersetting.