Algebra in superextensions of inverse semigroups
  We find necessary and sufficient conditions on an (inverse) semigroup $X$ under which its semigroups of maximal linked systems $\lambda(X)$, filters $\phi(X)$, linked upfamilies $N_2(X)$, and upfamilies $\upsilon(X)$ are inverse. 
Taras Banakh and Volodymyr Gavrylkiv
math.GR math.GN