대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
  • /
  • Pages.21-38
  • /
  • 2023
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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THE HOMOLOGY REGARDING TO E-EXACT SEQUENCES

  • 투고 : 2021.10.19
  • 심사 : 2022.06.15
  • 발행 : 2023.01.31
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초록

Let R be a commutative ring with identity. Let R be an integral domain and M a torsion-free R-module. We investigate the relation between the notion of e-exactness, recently introduced by Akray and Zebari [1], and generalized the concept of homology, and establish a relation between e-exact sequences and homology of modules. We modify some applications of e-exact sequences in homology and reprove some results of homology with e-exact sequences such as horseshoe lemma, long exact sequences, connecting homomorphisms and etc. Next, we generalize two special drived functor T or and Ext, and study some properties of them.

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참고문헌

  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. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992. https://doi.org/10.1007/978-1-4612-4418-9
  3. J. J. Rotman, An Introduction to Homological Algebra, Pure and Applied Mathematics, 85, Academic Press, Inc., New York, 1979.
  4. C. A. Weibel, History of homological algebra, in History of topology, 797-836, North-Holland, Amsterdam, 1999. https://doi.org/10.1016/B978-044482375-5/50029-8