• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-562
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• 1998

We prove the $C^r$ Closing Lemma for chain recurrence in compact surfaces.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.881-898
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• 2002

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.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.21-38
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• 2023

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.