DOI QR코드

DOI QR Code

EXACTNESS OF COCHAIN COMPLEXES VIA ADDITIVE FUNCTORS

  • Campanini, Federico (Dipartimento di Matematica "Tullio Levi-Civita" Universita di Padova) ;
  • Facchini, Alberto (Dipartimento di Matematica "Tullio Levi-Civita" Universita di Padova)
  • Received : 2020.02.24
  • Accepted : 2020.06.26
  • Published : 2020.10.31

Abstract

We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor P : Mod-R → Spec(Mod-R), where Spec(Mod-R) denotes the spectral category of Mod-R, and the localization functor with respect to the singular torsion theory.

Keywords

References

  1. I. Akray and A. Zebari, Essential exact sequences, Commun. Korean Math. Soc. 35 (2020), no. 2, 469-480. https://doi.org/10.4134/CKMS.c190243
  2. M. J. Arroyo Paniagua, A. Facchini, M. Gran, and G. Janelidze, What is the spectral category?, in "Rings and Factorizations", A. Facchini, M. Fontana, A. Geroldinger, and B. Olberding Eds., Springer, New York, 2020, pp. 135-152.
  3. A. Facchini, Module theory, Progress in Mathematics, 167, Birkhauser Verlag, Basel, 1998.
  4. T. Fritz, Categories of fractions revisited, Morfismos 15 (2011), no. 2, 19-38.
  5. P. Gabriel and U. Oberst, Spektralkategorien und regulare Ringe im von-Neumannschen Sinn, Math. Z. 92 (1966), 389-395. https://doi.org/10.1007/BF01112218
  6. P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergeb. Math. Grenzgeb, 35, Springer-Verlag New York, Inc., New York, 1967.
  7. K. R. Goodearl, Ring Theory, Marcel Dekker, Inc., New York, 1976.
  8. T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999. https://doi.org/10.1007/978-1-4612-0525-8
  9. B. Stenstrom, Rings of Quotients, Springer-Verlag, New York, 1975.