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Comultiplication modules over a pullback of Dedekind domains

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Abstract

First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if R is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication R-modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.

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References

  1. I. Assen, D. Simson and A. Skowroński: Representation Theory of Associative Algebra. Vol. 1. Techniques of Representation Theory. London Math. Soc. Student Texts 65, Cambridge Univ. Press, Cambridge-New York, 2007.

    Google Scholar 

  2. H. Ansari-Toroghy and F. Farshadifar: On endomorphisms of multiplication and comultiplication modules. Archivum Mathematicum 44 (2008), 9–15.

    MathSciNet  Google Scholar 

  3. H. Bass: On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–29.

    Article  MATH  MathSciNet  Google Scholar 

  4. Z. A. El-Bast and P. F. Smith: Multiplication modules. Comm. Algebra. 16 (1988), 755–779.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Ebrahimi Atani: On pure-injective modules over pullback rings. Comm. Algebra 28 (2000), 4037–4069.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Ebrahimi Atani: On secondary modules over pullback rings. Comm. Algebra 30 (2002), 2675–2685.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Ebrahimi Atani: On prime modules over pullback rings. Czech. Math. J. 54 (2004), 781–789.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Ebrahimi Atani and F. Farzalipour: Weak multiplication modules over a pullback of Dedekind domains. To appear in Colloq. Math.

  9. S. Ebrahimi Atani: Indecomposable weak multiplication modules over Dedekind domains. Demonstratio Mathematica XLI 41 (2008), 33–43.

    MATH  MathSciNet  Google Scholar 

  10. S. Ebrahimi Atani: On secondary modules over Dedekind domains. Southeast Asian Bull. Math. 25 (2001), 1–6.

    Article  MathSciNet  Google Scholar 

  11. A. Facchini and P. Vamos: Injective modules over pullbacks. J. London Math. Soc. 31 (1985), 125–138.

    Article  MathSciNet  Google Scholar 

  12. R. Kietpiński: On Γ-pure injective modules. Bull. Polon. Acad. Sci. Math. 15 (1967), 127–131.

    Google Scholar 

  13. L. Levy: Modules over pullbacks and subdirect sums. J. Algebra 71 (1981), 50–61.

    Article  MATH  MathSciNet  Google Scholar 

  14. L. Levy: Modules over Dedekind-like rings. J. Algebra 93 (1985), 1–116.

    Article  MATH  MathSciNet  Google Scholar 

  15. L. Levy: Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks. J. Algebra 70 (1981), 62–114.

    Article  Google Scholar 

  16. L. A. Nazarova and A. V. Roiter: Finitely generated modules over a dyad of local Dedekind rings and finite group having an abelian normal subgroup of index p. Izv. Acad. Nauk. SSSR 33 (1969), 65–89. (In Russian.)

    MATH  MathSciNet  Google Scholar 

  17. M. Prest: Model Theory and Modules. London Mathematical Society, Cambridge University Press, Cambridge, 1988.

    MATH  Google Scholar 

  18. M. Prest: Ziegler spectra of tame hereditary algebras. J. Algebra 207 (1998), 146–164.

    Article  MATH  MathSciNet  Google Scholar 

  19. D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories. Algebra, Logic and Applications. Vol. 4, Gordon and Breach Science Publishers, Switzerland-Australia, 1992.

    Google Scholar 

  20. D. Simson: On Corner type Endo-Wild algebras. J. Pure Appl. Algebra 202 (2005), 118–132.

    Article  MATH  MathSciNet  Google Scholar 

  21. R. Y. Sharp: Steps in Commutative Algebra. London Mathematical Society, Student Texts, Vol. 19, Cambridge University Press, Cambridge, 1990.

    MATH  Google Scholar 

  22. R. B. Warfield: Purity and algebraic compactness for modules. Pacific J. Math. 28 (1969), 699–719.

    MATH  MathSciNet  Google Scholar 

  23. A. N. Wiseman: Projective modules over pullback rings. Math. Proc. Cambridge Philos. Soc. 97 (1985), 399–106.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran

    Shahabaddin Ebrahimi Atani

  2. Faculty of Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

    Reza Ebrahimi Atani

Authors
  1. Reza Ebrahimi Atani
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  2. Shahabaddin Ebrahimi Atani
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Correspondence to Reza Ebrahimi Atani.

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Ebrahimi Atani, R., Ebrahimi Atani, S. Comultiplication modules over a pullback of Dedekind domains. Czech Math J 59, 1103–1114 (2009). https://doi.org/10.1007/s10587-009-0078-3

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  • DOI: https://doi.org/10.1007/s10587-009-0078-3

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