PORTUGALIAE MATHEMATICA Vol. 57, No. 3, pp. 325328 (2000) 

Uniserial GroupsShalom FeigelstockBarIlan University,Ramat Gan  ISRAEL Abstract: An abelian group $G$ is $E$cyclic (uniserial) if $G$ is a cyclic (uniserial) module over its endomorphism ring $E(G)$. In this note, abelian groups $G$ which are uniserial $R$modules, for $R$ a subring of $E(G)$, are studied. Results of J. Hausen on $E$uniserial groups are generalized to $R$uniserial groups. It will be shown that if $G$ is a finite rank reduced torsion free group, $R$ is a commutative subring of $E(G)$, satisfying $RG=G$, and $G$ is $R$uniserial, then $R$ is a domain whose lattice of ideals is totally ordered, and $G$ is the additive group of a ring isomorphic to $R$. Classification (MSC2000): 20K15. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 2000 Sociedade Portuguesa de Matemática
