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Search: MSC category 03C60 ( Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] )

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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

2. CMB 2002 (vol 45 pp. 71)

van den Dries, Lou; Kuhlmann, Franz-Viktor
Images of Additive Polynomials in $\FF_q ((t))$ Have the Optimal Approximation Property
We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings.

Categories:12J10, 12L12, 03C60

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