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Rings with indecomposable modules local

Surjeet Singh and Hind Al-Bleehed

Beiträge zur Algebra und Geometrie
Contributions to Algebra and GeometryVol. 45, No. 1, pp. 239-251 (2004)

Abstract: 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


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