A Lemma on Indecomposable Reflexive Modules and Applications

We characterize the indecomposable reflexive modules with respect to decomposable bimodules. As a consequence, we construct quite different bimodules admitting few reflexive modules. In particular, we show that a new class of bimodules with a cotilting-type behaviour studied by Mantese [ 9 ] , that is the class of locally quasi-cotilting bimodules, is extremely large.