On multiplicative automorphisms of incidence algebras

Abstract

Let [Formula: see text] be the incidence algebra of the preordered set [Formula: see text] over the ring [Formula: see text]. In the case of a finite connected partially ordered set [Formula: see text], we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra [Formula: see text]. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms.