Algebraic lattices of multiply $\Omega$-foliated Fitting classes

In this paper, we investigate the lattice of all Fitting classes, the lattice of all $n$-multiply $\Omega$-foliated Fitting classes with direction $\varphi$, $\psi_0\leq \varphi$, and the lattice of all totally canonical Fitting classes. It is shown that these lattices are algebraic with 1-generated compact elements.