Generalizations of Nakayama ring. IV: Left serial rings with (*,I) (Q1097942)

Let R be a left and right artinian ring with identity. An R-module M is called a uniserial module, if M has a unique composition series. If, for each primitive idempotent e, eR is uniserial, then R is called a right serial ring or Nakayama ring. The second author studied generalized Nakayama rings in a number of papers [ibid. 23, 181-200 (1986; Zbl 0588.16018), 523-539 (1986; Zbl 0612.16010)]. In this paper the authors assume that R is a left serial ring such that eJ/eJ 2 is square-free for each primitive idempotent e. In earlier papers of the second author the property: (*,n): Every maximal submodule of a direct sum of n hollow modules is also a direct sum of hollow modules [cf. \textit{M. Harada}, Osaka J. Math. 22, 81-98 (1985; Zbl 0559.16010)] was introduced. In this paper a characterization of a left serial ring with (*,1) as a right R- module is given.