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 pure injective indecomposable module, local dual, generic module, amalgamation

MSC Classifications:

16G10, 03C60 show english descriptions Representations of Artinian rings
Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 16G10 - Representations of Artinian rings
03C60 - Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]

top of page | contact us | social media | privacy | site map