Rings and constructions of partial difference sets

We present three constructions of partial difference sets (PDS) using different types of finite local rings. The first construction uses homomorphic images of finite Frobenius local rings and generalizes a previous result by the author. The second construction uses finite Frobenius local rings. The third construction uses finite (noncommutative) chain rings and generalizes a recent construction of partial difference sets by Leung and Ma. The three constructions provide many new PDS in nonelementary abelian groups.