Inner automorphisms of Clifford monoids

An automorphism q5 of a monoid S is called inner if there exists g in U S , the group of units of S , such that / ( 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.