Skew Incidence Rings and the Isomorphism Problem

Abstract

Let [Formula: see text] be a finite partially ordered set, [Formula: see text] an associative unital ring and [Formula: see text] an endomorphism of [Formula: see text]. We describe some properties of the skew incidence ring [Formula: see text] such as invertible elements, idempotents, the Jacobson radical and the center. Moreover, if two skew incidence rings [Formula: see text] and [Formula: see text]are isomorphic and the only idempotents of [Formula: see text] and [Formula: see text] are the trivial ones, we show that the partially ordered sets [Formula: see text] and [Formula: see text] are isomorphic.