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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, amalgamationCategories:16G10, 03C60

2. CMB 1998 (vol 41 pp. 71)

Hurrelbrink, Jurgen; Rehmann, Ulf
 Splitting patterns and trace forms The splitting pattern of a quadratic form $q$ over a field $k$ consists of all distinct Witt indices that occur for $q$ over extension fields of $k$. In small dimensions, the complete list of splitting patterns of quadratic forms is known. We show that {\it all\/} splitting patterns of quadratic forms of dimension at most nine can be realized by trace forms. Keywords:Quadratic forms, Witt indices, generic splitting.Category:11E04
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