Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 239251 (2004) 

Rings with indecomposable modules localSurjeet Singh and Hind AlBleehedDepartment of Mathematics, King Saud University, PO Box 2455, Riyadh 11451, Saudi ArabiaAbstract: Every indecomposable module over a generalized uniserial ring is uniserial and hence a local module. This motivates us to study rings $R$ satisfying the following condition: $(*)$ $R$ is a right artinian ring such that every finitely generated right $R$module is local. The rings $R$ satisfying $(*)$ were first studied by Tachikawa in 1959, by using duality theory, here they are endeavoured to be studied without using dualtity. Structure of a local right $R$module and in particular of an indecomposable summands of $R_{R}$ is determined. Matrix representation of such rings is discussed. Keywords: left serial rings, generalized uniserial rings, exceptional rings, uniserial modules, injective modules, injective cogenerators and quasiinjective modules Classification (MSC2000): 16G10; 16P20 Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
