Aydogdu, PinarEr, NoyanErtas, Nil Orhan2024-09-292024-09-2920120017-08951469-509Xhttps://doi.org/10.1017/S0017089512000183https://hdl.handle.net/20.500.14619/5453Dedekind domains, Artinian serial rings and right uniserial rings share the following property: Every cyclic right module is a direct sum of uniform modules. We first prove the following improvement of the well-known Osofsky-Smith theorem: Acyclic module with every cyclic subfactor a direct sum of extending modules has finite Goldie dimension. So, rings with the above-mentioned property are precisely rings of the title. Furthermore, a ring R is right q.f.d. (cyclics with finite Goldie dimension) if proper cyclic (not congruent to R-R) right R-modules are direct sums of extending modules. R is right serial with all prime ideals maximal and boolean AND(n is an element of N)J(n) = J(m) for some m is an element of N if cyclic right R-modules are direct sums of quasi-injective modules. A right non-singular ring with the latter property is right Artinian. Thus, hereditary Artinian serial rings are precisely one-sided non-singular rings whose right and left cyclic modules are direct sums of quasi-injectives.eninfo:eu-repo/semantics/openAccessArticle10.1017/S00170895120001832-s2.0-848645438796173Q260554WOS:000307171200010Q3