| Authors | Ebrahim Nasrabadi,Kianoush Kazem |
|---|---|
| Journal | Boletim da Sociedade Paranaense de Matematica |
| Page number | 1-7 |
| Serial number | 43 |
| Volume number | 3 |
| Paper Type | Full Paper |
| Published At | 2025 |
| Journal Type | Typographic |
| Journal Country | Albania |
| Journal Index | Scopus |
Abstract
Let $S$ be a discrete semigroup with idempotent set $E$ and $T$ be a left multiplier operator on $S$, which makes it a newly induced semigroup $S _{T}$ with idempotent set $E_T$. In this paper while examining the properties of inducted semigroup algebra $ \ell^1({S_{T}}) $, we show that under certain conditions for $T$, the first cyclic cohomology groups $ \HH\CC^{1}(\ell^1(S), \ell^{\infty}(S))$ and $\HH\CC^{1}(\ell^1({S_{T}}), \ell^{\infty}(S_{T})) $ are equal, where $S$ be a monoid semigroup. We also show in another section, when $ S $ is a completely regular semigroup, then the semigroup algebra $ \ell^1({S_{T}}) $ is cyclic amenable. Finally, by providing examples at the end of each section, we examine the conditions raised in this paper.