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Preprint Number 1573
1573. Thomas G. Kucera and Marcos Mazari-Armida On universal modules with pure embeddings E-mail: Submission date: 1 March 2019 Abstract: We show that certain classes of modules have universal models with respect to pure embeddings.
Theorem. Let R be a ring, T a first-order theory with an infinite model
extending the theory of R-modules and K^T=(Mod(T), ≤_{pp}) (where
≤_{pp} stands for pure submodule). Assume K^T has joint embedding and
that pure-injective modules are amalgamation bases. If λ^{|T|}=λ
or ∀ μ < λ( μ^{|T|} < λ), then K^T has a universal
model of cardinality λ.
Mathematics Subject Classification: 03C45, 03C48, 03C60, 13L05, 16D10 Keywords and phrases: |

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