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Articles

Duality pairs and FP-injective modules over formal triangular matrix rings

Pages 5296-5310 | Received 16 Oct 2019, Accepted 20 Jun 2020, Published online: 09 Jul 2020

References

  • Asadollahi, J., Salarian, S. (2006). On the vanishing of Ext over formal triangular matrix rings. Forum Math. 18:951–966.
  • Auslander, M., Bridge, M. (1969). Stable Module Theory. Mem. Amer. Math. Soc. 94, Providence, RI.: Amer. Math. Soc.
  • Auslander, M., Reiten, I., Smalo, S. O. (1995). Representation Theory of Artin Algebras. Cambridge Stud. Adv. Math. 36, Cambridge: Cambridge University Press.
  • Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring. arXiv:1405.5768.
  • Cheatham, T. J., Stone, D. R. (1981). Flat and projective character modules. Proc. Amer. Math. Soc. 81(2):175–177. DOI: 10.1090/S0002-9939-1981-0593450-2.
  • Enochs, E. E., Jenda, O. M. G. (2000). Relative Homological Algebra. Berlin-New York: Walter de Gruyter.
  • Fieldhouse, D. J. (1972). Character modules, dimension and purity. Glasgow Math. J. 13(2):144–146. DOI: 10.1017/S0017089500001567.
  • Fossum, R. M., Griffith, P., Reiten, I. (1975). Trivial Extensions of Abelian Categories, Homological Algebra of Trivial Extensions of Abelian Categories with Applications to Ring Theory. Lect. Notes in Math. 456, Berlin: Springer-Verlag.
  • Gillespie, J. (2019). Duality pairs and stable module categories. J. Pure Appl. Algebra 223(8):3425–3435. DOI: 10.1016/j.jpaa.2018.11.010.
  • Göbel, R., Trlifaj, J. (2006). Approximations and Endomorphism Algebras of Modules. GEM 41, Berlin-New York: Walter de Gruyter.
  • Goodearl, K. R. (1976). Ring Theory: Nonsingular Rings and Modules. Monographs Textbooks Pure Appl. Math. 33, New York and Basel: Marcel Dekker, Inc.
  • Goodearl, K. R., Warfield, R. B. Jr., (2004). An Introduction to Noncommutative Noetherian Rings. London Math. Soc. Student Texts, p. 61. Cambridge: Cambridge University Press.
  • Green, E. L. (1982). On the representation theory of rings in matrix form. Pacific J. Math. 100(1):123–138. DOI: 10.2140/pjm.1982.100.123.
  • Haghany, A., Mazrooei, M., Vedadi, M. R. (2012). Pure projectivity and pure injectivity over formal triangular matrix rings. J. Algebra Appl. 11(06):1250107–1250113. DOI: 10.1142/S0219498812501071.
  • Haghany, A., Varadarajan, K. (1999). Study of formal triangular matrix rings. Commun. Algebra 27(11):5507–5525. DOI: 10.1080/00927879908826770.
  • Haghany, A., Varadarajan, K. (2000). Study of modules over formal triangular matrix rings. J. Pure Appl. Algebra 147(1):41–58. DOI: 10.1016/S0022-4049(98)00129-7.
  • Holm, H., Jørgensen, P. (2009). Cotorsion pairs induced by duality pairs. J. Commut. Algebra 1(4):621–633. DOI: 10.1216/JCA-2009-1-4-621.
  • Krylov, P., Tuganbaev, A. (2017). Formal Matrices. Switzerland: Springer International Publishing.
  • Lam, T. Y. (1999). Lectures on Modules and Rings. New York-Heidelberg-Berlin: Springer-Verlag.
  • Megibben, C. (1970). Absolutely pure modules. Proc. Amer. Math. Soc. 26(4):561–566. DOI: 10.1090/S0002-9939-1970-0294409-8.
  • Rotman, J. J. (1979). An Introduction to Homological Algebra. New York: Academic Press.
  • Stenström, B. (1970). Coherent rings and FP-injective modules. J. London Math. Soc. s2-2(2):323–329. DOI: 10.1112/jlms/s2-2.2.323.

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