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A Note on Regular Objects in Grothendieck Categories

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Abstract

We study relative regular objects with respect to a generator in a Grothendieck category which is not necessarily locally finitely generated. Using the Gabriel–Popescu Theorem, we extend results known for regular modules.

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References

  1. Dăscălescu S., Năstăsescu C., Tudorache A., Dăuş L.: Relative regular objects in categories. Appl. Categ. Struct 14, 567–577 (2006)

    Article  MATH  Google Scholar 

  2. Zelmanowitz J.: Regular modules. Trans. Am. Math. Soc 163, 341–355 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mac Lane S.: Categories for the Working Mathematician, Graduate Texts in Mathematics, vol. 5. Springer, New York (1998)

    Google Scholar 

  4. Gabriel P.: Des Catégories Abéliennes. Bull. Soc. Math. Fr 90, 323–448 (1962)

    MathSciNet  MATH  Google Scholar 

  5. Popescu, N.: Abelian Categories with Applications to Rings and Modules, L.M.S. Monographs, vol. 3. Academic Press, London. XII (1973)

  6. Brzeziński T., Wisbauer R.: Corings and Comodules, London Mathematical Society Lecture Note Series, vol. 309. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  7. Năstăsescu C., Van Oystaeyen F.: Methods of Graded Rings, Lecture Notes in Mathematics, vol 1836. Springer, Berlin (2004)

    Google Scholar 

  8. Stenström B.: Purity in functor categories. J. Algebra 8, 352–361 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fieldhouse D.: Pure theories. Math. Ann. 184, 1–18 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fieldhouse D.: Regular modules and rings. Ill. J. Math. 16, 217–221 (1972)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 010014, Bucharest 1, Romania

    S. Dăscălescu & C. Năstăsescu

  2. Universitatea de Ştiinţe Economice, Bucharest, Romania

    A. Tudorache

Authors
  1. S. Dăscălescu
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  2. C. Năstăsescu
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  3. A. Tudorache
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Corresponding author

Correspondence to S. Dăscălescu.

Additional information

The research of S. Dăscălescu and A. Tudorache was supported by Grant ID-1904, contract 479/13.01.2009 of CNCSIS.

C. Năstăsescu was partially supported by the CEEX program of the Romanian Ministry of Education and Research, contract 2-CEx06-11-20.

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Dăscălescu, S., Năstăsescu, C. & Tudorache, A. A Note on Regular Objects in Grothendieck Categories. Arab J Sci Eng 36, 957–962 (2011). https://doi.org/10.1007/s13369-011-0098-9

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  • DOI: https://doi.org/10.1007/s13369-011-0098-9

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