Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 1, pp. 239-251 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 239-251 (2004) |
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Rings with indecomposable modules localSurjeet Singh and Hind Al-BleehedDepartment 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 quasi-injective 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
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