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# Ziegler's Indecomposability Criterion

Published:2011-12-16
Printed: Sep 2013
• Ivo Herzog,
The Ohio State University at Lima, Lima, OH 45804, USA
 Format: LaTeX MathJax PDF

## Abstract

Ziegler's Indecomposability Criterion is used to prove that a totally transcendental, i.e., $\Sigma$-pure injective, indecomposable left module over a left noetherian ring is a directed union of finitely generated indecomposable modules. The same criterion is also used to give a sufficient condition for a pure injective indecomposable module ${_R}U$ to have an indecomposable local dual $U_R^{\sharp}.$
 Keywords: pure injective indecomposable module, local dual, generic module, amalgamation
 MSC Classifications: 16G10 - Representations of Artinian rings 03C60 - Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]