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.
idempotents center nearly complete inner automorphisms structure homomorphisms semilattice of groups
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Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Proje Numarası | NA |
Erken Görünüm Tarihi | 14 Nisan 2024 |
Yayımlanma Tarihi | 27 Ağustos 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 4 |