2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114258In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.6 pages, minor changes, to appear in Bull. London Math. SocCommutative Algebra13C13, 13D05, 16G60text