A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence of non-standard uniserial modules; this is a theorem of ZFC which complements an earlier independence result.

A serial ring (generalized uniserial in the terminology of Nakayama) is one whose left and right free modules are direct sums of modules with unique finite composition series (uniserial modules.) This paper presents a module-theoretic discussion of the structure of serial rings, and some onesided characterizations of certain kinds of serial rings. As an application of the structure theory, an e...

Abstract In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a group admits non-canonical structure if and only its isometry has dimension four.

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three twosided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω1-generated uniserial module over every non-artini...

The paper must have abstract. In this paper we continue the investigations on morphic groups. We also show that if a group is normaly uniserial and of order p3 with p prime it must be morphic and so give a negative answer to one of the questions of [4]. We caractrize the morphic groups of order p3 with p an odd prime. We also explore the set of subgroups of a morphic group which still morphic b...

We consider the question of which valuation domains (of cardinality א1) have nonstandard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ZFC + GCH. 1991 Mathematics Subject Classification. Primary 13L05, 03E35, 13C05; Secondary 03E75, 13A18.