Bulletin of the Korean Mathematical Society (대한수학회보)

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SEMI-DIVISORIALITY OF HOM-MODULES AND INJECTIVE COGENERATOR OF A QUOTIENT CATEGORY

  • Kim, Hwan-Koo (Department of Information Security Hoseo University)
  • Received : 2009.07.31
  • Published : 2011.03.31
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Abstract

In this paper, we study w-ity and (co-)semi-divisoriality of Hom-modules and the semi-divisorial envelope of $Hom_R$(M,N) under suitable conditions on R, M, and N. We also investigate an injective cogenerator of a quotient category.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. I. Beck, Injective modules over a Krull domain, J. Algebra 17 (1971), 116-131. https://doi.org/10.1016/0021-8693(71)90048-2
  2. L. Fuchs and L. Salce, Modules over Non-Noetherian Domains, Mathematical Surveys and Monographs 84, AMS, Providence, RI, 2001.
  3. R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, Ontario, 1992.
  4. S. Glaz and W. V. Vasconcelos, Flat ideals II, Manuscripta Math. 22 (1977), no. 4, 325-341. https://doi.org/10.1007/BF01168220
  5. S. Glaz and W. V. Vasconcelos, Flat ideals III, Comm. Algebra 12 (1984), no. 1-2, 199-227. https://doi.org/10.1080/00927878408822998
  6. J. S. Golan, Localizations of Noncommutative Rings, Marcel Dekker, New York, 1975.
  7. H. Kim, Module-theoretic characterizations of t-linkative domains, Comm. Algebra, 36 (2008), no. 5, 1649-1670. https://doi.org/10.1080/00927870701872513
  8. H. Kim, Module-theoretic characterizations of generalized GCD domains, Comm. Algebra, 38 (2010), no. 2, 759-772. https://doi.org/10.1080/00927870902828660
  9. H. Kim, E. S. Kim, and Y. S. Park, Injective modules over strong Mori domains, Houston J. Math. 34 (2008), no. 2, 349-360.
  10. J. L. B. Montero, B. T. Jover, and A. Verschoren, Local Cohomology and Localization, Pitman Research Notes in Mathematics Series, 226, Longman Scientic & Technical, London, 1989.
  11. M. Moucouf, Some results on injective modules over a ring of Krull type, Comm. Algebra 33 (2005), no. 11, 4125-4133. https://doi.org/10.1080/00927870500261439
  12. M. Nishi and M. Shinagawa, Codivisorial and divisorial modules over completely integrally closed domains. I, Hiroshima Math. J. 5 (1975), no. 2, 269-292.
  13. M. Nishi and M. Shinagawa, Codivisorial and divisorial modules over completely integrally closed domains. II, Hiroshima Math. J. 5 (1975), no. 3, 461-471.
  14. B. Stenstrom, Rings of Quotients: An Introduction to Methods of Ring Theory,Springer-Verlag, New York, 1973.
  15. R. G. Swan, Algebraic K-theory, Lecture notes in Math. 76, Springer-Verlarg, New York, 1968.
  16. F. Wang, On w-projective modules and w-at modules, Algebra Colloq. 4 (1997), no. 1, 111-120.
  17. F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra 25 (1997), no. 4, 1285-1306. https://doi.org/10.1080/00927879708825920