Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

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...

If R is a commutative ring, then we prove that every finitely generated R-module has a pure-composition series with indecomposable cyclic factors and any two such series are isomorphic if and only if R is a Bézout ring and a CF-ring. When R is a such ring, the length of a pure-composition series of a finitely generated R-module M is compared with its Goldie dimension and we prove that these num...

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.

Let A be an associative algebra over a field K such that the dimension, [A:P], of A over K is finite. Following the terminology of [8], we shall say that A is of bounded module type if there exists an integer re such that for every indecomposable left A-module M, the inequality [M: K] zí re holds. The algebra A is of finite module type if A has only a finite number of nonisomorphic indecomposab...