Inner Automorphisms of Clifford Monoids

Abstract

An automorphism ϕ of a monoid S is called inner if there exists g in US, the
 group of units of S, such that ϕ(s) = gsg−1 for all s in S; we call S nearly
 complete if all of its automorphisms are inner. In this paper, first, we prove
 several results on inner automorphisms of a general monoid and subsequently
 apply them to Clifford monoids. For certain subclasses of the class of Clifford
 monoids, we give necessary and sufficient conditions for a Clifford monoid to
 be nearly complete. These subclasses arise from conditions on the structure
 homomorphisms of the Clifford monoids: all being either bijective, surjective,
 injective, or image trivial.