文摘
We show that for an inverse semigroup S with the set idempotents E acting on S trivially from left and by multiplication from right, any bounded module derivation from \(\ell ^1(S)\) to \(({\ell ^1(S)}/{J})^*=J^{\perp }\) is inner, where J is the closed ideal generated by elements of the form \(\delta _{set}-\delta _{st}\) with \(s,t\in S\) and \(e\in E\).