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The Torsion Theory and the Melkersson Condition

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Abstract

We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition appears in the context of torsion theories.

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References

  1. M. Aghapournahr, L. Melkersson: Local cohomology and Serre subcategories. J. Algebra 320 (2008), 1275–1287.

    Article  MathSciNet  Google Scholar 

  2. A. Beligiannis, I. Reiten: Homological and homotopical aspects of torsion theories. Mem. Am. Math. Soc. 883 (2007), 207 pages.

    MathSciNet  MATH  Google Scholar 

  3. S. E. Dickson: A torsion theory for Abelian categories. Trans. Am. Math. Soc. 121 (1966), 223–235.

    Article  MathSciNet  Google Scholar 

  4. P. Gabriel: Des catégories abéliennes. Bull. Soc. Math. Fr. 90 (1962), 323–448. (In French.)

    Article  Google Scholar 

  5. J. Lambek: Torsion Theories, Additive Semantics, and Rings of Quotients. Lecture Notes in Mathematics 177, Springer, Berlin, 1971.

    Book  Google Scholar 

  6. B. Stenström: Rings and Modules of Quotients. Lecture Notes in Mathematics 237, Springer, Berlin, 1971.

    Book  Google Scholar 

  7. B. Stenström: Rings of Quotients. An Introduction to Methods of Ring Theory. Die Grundlehren der Mathematischen Wissenschaften 217, Springer, Berlin, 1975.

    MATH  Google Scholar 

  8. T. Yoshizawa: Subcategories of extension modules by Serre subcategories. Proc. Am. Math. Soc. 140 (2012), 2293–2305.

    Article  MathSciNet  Google Scholar 

  9. T. Yoshizawa: On the closedness of taking injective hulls of several Serre subcategories. Commun. Algebra 45 (2017), 4846–4854.

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The author expresses gratitude to the referees for their kind comments and valuable suggestions.

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Authors and Affiliations

  1. National Institute of Technology, Toyota College, 2-1 Eiseicho, Toyota, Aichi, Japan, 471-8525

    Takeshi Yoshizawa

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  1. Takeshi Yoshizawa
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Correspondence to Takeshi Yoshizawa.

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Yoshizawa, T. The Torsion Theory and the Melkersson Condition. Czech Math J 70, 121–145 (2020). https://doi.org/10.21136/CMJ.2019.0193-18

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  • DOI: https://doi.org/10.21136/CMJ.2019.0193-18

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