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1. CMB 2011 (vol 56 pp. 564)

Herzog, Ivo
Ziegler's Indecomposability Criterion
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
Categories:16G10, 03C60

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