Generalizations of Nakayama ring. V: Left serial rings with (*,2) (Q1092146)

In this paper the author continues his study of left serial rings, which are generalizations of Nakayama rings. In a paper with \textit{Y. Baba} left serial rings with (*,1) were investigated [Part IV, ibid. 24, 139-145 (1987)]. Here the condition (*,n) is defined as follows: Every maximal submodule of a direct sum of n hollow modules is also a direct sum of hollow modules [cf. Part I, ibid. 23, 181-200 (1986; Zbl 0588.16018)]. In this paper, a certain characterization of a left serial ring R with (*,1) and of a ring R with (*,2) is obtained. In an earlier paper a characterization of a certain artinian ring with (*,3) was given [Part II, ibid. 23, 509-521 (1986; Zbl 0612.16009)].