On Pure-Injective Modules

  • E. Monari Martinez
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)


Some results on pure-injective modules over a commutative ring with 1, proved by Ziegler using model theory, are proved here through algebraic methods. As application of these results we obtain again the structure of indecomposable pure-injective modules over a valuation domain, showing that their elements have constant indicator.


Commutative Ring Small Extension Valuation Domain Injective Envelope Limit Height 


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  1. [1]
    L. Fuchs and L. Salce “Prebasic submodules over valuation rings” Annali Mat. Pura Appl. 32. (1982) 257–274.CrossRefMathSciNetGoogle Scholar
  2. [2]
    R. B. Warfield, jr. “Purity and algebraic compactness for modules” Pacific J. Math. 28 , No. 3, 1969, 699–719.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    M. Ziegler “Model theory of modules” Annals Pure Appl. Logic, 26 (1984), 149–213.CrossRefMATHGoogle Scholar
  4. [4]
    B. Zimmermann-Huisgen and W. Zimmermann “Algebraically compact ring and modules” Math. Zeitschrift 161 (1978) 81–93.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • E. Monari Martinez
    • 1
  1. 1.Universita’ di PadovaItaly

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