Inner automorphisms of Clifford monoids

Year 2024, Volume: 53 Issue: 4, 1060 - 1074, 27.08.2024

Aftab Shah , Dilawar Mir Thomas Quinn-gregson

https://doi.org/10.15672/hujms.1244782

Cited By: 1

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

Supporting Institution

NA

Project Number

NA

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