  This article addresses the issue of the closure of the algebra of constraints
for generic (cosmological) perturbations when taking into account
simultaneously the two main corrections of effective loop quantum cosmology,
namely the holonomy and the inverse-volume terms. Previous works on either the
holonomy or the inverse volume case are reviewed and generalized. In the
inverse-volume case, we point out new possibilities. An anomaly-free solution
including both corrections is found for perturbations, and the corresponding
equations of motion are derived.
