Faithful distributive modules over incidence algebras

Abstract

Let Q be a lower finite quasi-ordered set and let I(Q) be the incidence algebra of Q over a field K. In this paper we determine all faithful distributive modules over I(Q) and relate the result to the structure of the outer automorphism group of the algebra. In the case when Q is finite we also determine all left ideals L of I(Q) such that nQ) I{Q)IL is a faithful distributive module over I(Q).