Inner automorphisms of Clifford monoids

Authors : Aftab Shah, Dilawar Mir, Thomas Quinn-gregson

Pages : 1060-1074

Doi:10.15672/hujms.1244782

View : 145 | Download : 180

Publication Date : 2024-08-27

Article Type : Research Paper

Abstract :An automorphism $\\phi$ of a monoid $S$ is called inner if there exists $g$ in $U_{S}$, the group of units of $S$, such that $\\phi(s)=gsg^{-1}$ 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.
Keywords : idempotents, center, nearly complete, inner automorphisms, structure homomorphisms, semilattice of groups