Generalizations of Nakayama ring. VI: Right US-n rings; \(n=3,4\) (Q1097943)

[For part IV see the preceding review.] Let R be an artinian ring. In an earlier paper the author generalized the concept of right serial ring (Nakayama ring) considering (**,n): Every maximal submodule in a direct sum D of n hollow modules contains a non- zero direct summand of D [cf. Part I, Osaka J. Math. 23, 181-200 (1986; Zbl 0588.16018)]. If (**,n) holds for any direct sum of n hollow modules, then R is called a right US-n ring (cf. the cited paper). In this paper a complete list of right US-3 (resp. US-4) rings is given, satisfying one extra condition. The characterizations are illustrated at the end of the paper by several examples.