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Pure Injective Modules over a Commutative Valuation Domain

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Abstract

Using geometrical invariants we classify those pure injective modules over a commutative valuation domain which are envelopes of one element.

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References

  1. Eklof, P. and Herzog, I.: Some model theory over a serial ring, Ann. Pure Appl. Logic 72 (1995), 145–176.

    Google Scholar 

  2. Fuchs, L. and Salce, L.: Modules over Valuation Domains, Lecture Notes in Pure Appl. Math. 97, Dekker, New York, 1985.

    Google Scholar 

  3. Facchini, A.: Decompositions of algebraically compact modules, Paci fic J. Mat h. 116(1) (1985), 25–37.

    Google Scholar 

  4. Goodearl, K. R.: Von Neumann Regular Rings, Pitman, London, 1979.

    Google Scholar 

  5. Puninski, G. E.: Superdecomposable pure injective modules over commutative valuation rings, Algebra i Logika 31(6) (1992), 377–386.

    Google Scholar 

  6. Puninski, G. E.: Indecomposable pure injective modules over chain rings, Trans. Moscow Math. Soc. 56 (1995), 137–147.

    Google Scholar 

  7. Puninski, G.: Serial Rings, Kluwer Acad. Publ., Dordrecht, 2001.

    Google Scholar 

  8. Prest, M.: Model Theory and Modules, London Math. Soc. Lecture Note Ser. 130, Cambridge Univ. Press, 1988.

  9. Salce, L.: Valuation domains with superdecomposable pure injective modules, In: Lecture Notes in Pure Appl. Math. 146, Dekker, New York, 1993, pp. 241–245.

    Google Scholar 

  10. Tuganbaev, A. A.: Semidistributive Rings and Modules, Math. Appl. 449, Kluwer Acad. Publ., Dordrecht, 1998.

    Google Scholar 

  11. Ziegler, M.: Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149–213.

    Google Scholar 

  12. Zimmermann-Huisgen, B. and Zimmermann, W.: Algebraically compact rings and modules, Math. Z. 161 (1978), 81–93.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University at Lima, 435 Galvin Hall, 4240 Campus Drive, Lima, OH, 45804, U.S.A

    Gena Puninski

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  1. Gena Puninski
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Puninski, G. Pure Injective Modules over a Commutative Valuation Domain. Algebras and Representation Theory 6, 239–250 (2003). https://doi.org/10.1023/A:1025186829954

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  • DOI: https://doi.org/10.1023/A:1025186829954

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