Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A GENERALIZATION OF HOMOLOGICAL ALGEBRA

  • Davvaz, B. (Department of Mathematics, Yazd University) ;
  • Shabani-Solt, H. (Department of Mathematics, Yazd University)
  • Published : 2002.11.01
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Abstract

Our aim in this paper is to introduce a generalization of some notions in homological algebra. We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and $\mu$-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.

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References

  1. Far East J. Math. Sci.(FJMS) v.4 no.2 U-Split Exact Sequences S. M. Anvariyeh;B. Davvaz
  2. Bull. Malaysian Math. Soc. v.22 no.2 A Note on Exact Sequences B. Davvaz;Y. A. Parnian-Gramaleky
  3. Algebra Universalis v.35 Hypergroups de type U et homologie de complexes D. Freni;Y. Sureau https://doi.org/10.1007/BF01190968
  4. Second Edition A Course in Homological Algebra P. J. Hilton;U. Stammbach
  5. Canad. Math. Bull. v.7 Goursat's Theorem and Homological Algebra J. Lambek https://doi.org/10.4153/CMB-1964-055-7
  6. An Introduction to Homological Algebra J. J. Rotman

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