Skew Incidence Rings and the Isomorphism Problem

Let X be a finite partially ordered set, R an associative unital ring and sigma an endomorphism of R. We describe some properties of the skew incidence ring I(X,R,sigma) such as invertible elements, idempotents, the Jacobson radical and the center. Moreover, if two skew incidence rings I(X,R,sigma) and I(Y,S,tau)are isomorphic and the only idempotents of R and S are the trivial ones, we show that the partially ordered sets X and Y are isomorphic.