Addendum to‎: "‎Infinite-dimensional versions of the primary‎, ‎cyclic and Jordan‎ ‎decompositions"‎, ‎by M‎. ‎Radjabalipour

‎In his paper mentioned in the title‎, ‎which appears in the same issue of this‎ ‎journal‎, ‎Mehdi Radjabalipour derives the cyclic decomposition of an algebraic‎ ‎linear transformation‎. ‎A more general structure theory for linear‎ ‎transformations appears in Irving Kaplanskyʹs lovely 1954 book on infinite‎ ‎abelian groups‎. ‎We present a translation of Kaplanskyʹs results for abelian‎ ‎groups into the terminology of linear transformations‎. ‎We add an additional‎ ‎translation of a ring-theoretic result to give a characterization of‎ ‎algebraically hyporeflexive transformations and the strict closure of the set‎ ‎of polynomials in a transformation $T$‎. ‎