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Original Articles

A classification of torsion classes in abelian categories

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Pages 502-515 | Received 04 Apr 2018, Accepted 14 May 2018, Published online: 16 Oct 2018

References

  • Gabriel, P. (1962). Des catégories abéliennes. Bul. Soc. Math. France 79:323–448.
  • Beilinson, A. A., Bernstein, J., Deligne, P. (1982). Faiscearx pervers. Asterisque 100:5–171.
  • Stanley, D. (2010). Invariants of t-structures and classification of nullity classes. Adv. Math. 224(6):2662–2689.
  • Tarrio, L. A., Lopez, A. J., Saorin, M. (2010). Compactly generated t-structures on the derived category of a Noetherian ring. J. Algebra 324(3):313–346.
  • Neeman, A., Bökstedt, M. (1992). The chromatic tower for D(R). Topology 31(3):519–532.
  • Neeman, A. (2011). Colocalizing subcategorie of D(R). J. Reine Angewandte Math. 653:221–243.
  • Balmer, P. (2005). The spectrum of prime ideals in tensor triangulated categories. J. Angewandte Math. 2005(588):149–168.
  • Rosenberg, A. (1996). Reconstruction of Schemes. Munich, Germany: Max Planck Institute.
  • Rouquier, R. (2010). Derived categories and algebraic geometry. In: Holm, T., Jorgensen, P., Rouquier, R., eds. Triangulated Categories, Volume 375 of London Mathematical Society Lecture Note Series. Cambridge, UK: Cambridge University Press, pp. 351–370.
  • Kanda, R. (2012). Classifying Serre subcategories via atom spectrum. Adv. Math. 231(3–4):1572–1588.
  • Tiwary, A. K., Pandeya, B. M. (1984). Modules whose nonzero endomorphisms are monomorphisms. In: Manocha, H. L., Srivastava, J. B., eds. Algebra and Its Appliations, Volume 91 of Lecture Notes in Pure and Applied Mathematics. New York, NY: Marcel Dekker, Inc.
  • Xue, W. (1994). On morita duality. Baz. Society 49(01):35–45.
  • Gordon, R., Robson, J. C. (1973). Krull Dimension, Volume 133 of Memoirs of the American Mathematical Society. Providence, RI: American Mathematical Society.
  • Storrer, H. H. (1972). On Goldman’s primary decomposition. In: Dold, A., Eckmann, B., eds. Lectures on Rings and Modules, Volume 246 of Lecture Notes in Mathematics. Zurich: Springer, pp. 617–661.
  • Goldman, O. (1969). Rings and modules of quotients. J. Algebra 13(1):10–47.
  • Lam, T. Y. (1998). Lectures on Modules and Rings, Volume 189 of Graduate Text in Mathematics. New York: Springer.
  • M., Reyes, A. (2010). One-sided prime ideal principal for noncommutative rings. J. Algebra Appl. 9(06):877.
  • Stanley, D., Wang, B. (2011). Classifying subcategories of finitely generated modules over a noetherian ring. J. Pure Appl. Algebra 215(11):2684–2693.
  • Beligiannis, A., Reiten, I. (2007). Homological and homotopical aspects of torsion theories, volume 188 of memoirs of the American Mathematical Society. Mem. Ams. Soc. 188(883):207.
  • Neeman, A. (2001). Triangulated Categories, Volume 148 of Annals of Mathematics Studies. Princeton, NJ: Princeton University Press.
  • Dickson, S. E. (1966). A torsion theory for abelian categories. Trans. Amer. Math. Soc. 121(1):223–235.
  • Assem, I., Simson, D., Skowronski, A. (2006). Elements of the Representation Theory of Associative Algebra, Volume 65 of London Mathematical Society Student Texts. Cambridge: Cambridge University Press.
  • Eisenbud, D. (1994). Commutative Algebra with a View toward Algebraic Geometry, Volume 150 of Graduate Texts in Mathematics. New York: Springer.
  • Atiyah, M. F., MacDonald, I. G. (1969). Introduction to Commutative Algebra. Reading, MA: Addison-Wesley.
  • Stanley, D., Wang, B. (2009). Nullity classes and the nullification functor of modules. Preprint, November.
  • Hilton, P. J., Stanmmbach, U. (1970). A Course in Homological Algebra, Volume 4 of Graduate Text in Mathematics. New York: Springer-Verlag.
  • Davey, B. A., Priestley, H. A. (2002). Introduction to Lattices and Order. Cambridge, UK: Cambridge University Press.

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