• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.469-480
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• 2020

Let R be a commutative ring with identity and M a unital R-module. We give a new generalization of exact sequences called e-exact sequences. A sequence $0{\rightarrow}A{\longrightarrow[20]^f}B{\longrightarrow[20]^g}C{\rightarrow}0$ is said to be e-exact if f is monic, Imf ≤_e Kerg and Img ≤_e C. We modify many famous theorems including exact sequences to one includes e-exact sequences like 3 × 3 lemma, four and five lemmas. Next, we prove that for torsion-free module M, the contravariant functor Hom(-, M) is left e-exact and the covariant functor M ⊗ - is right e-exact. Finally, we define e-projective module and characterize it. We show that the direct sum of R-modules is e-projective module if and only if each summand is e-projective.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.149-155
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• 2005

The notion of U-exact sequence (or quasi-exact sequence) of modules was introduced by Davvaz and Parnian-Garamaleky as a generalization of exact sequences. In this paper, we prove further results about quasi-exact sequences. In particular, we give a generalization of Schanuel's Lemma. Also we obtain some relation-ship between quasi-exact sequences and superfluous (or essential) submodules.

• 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.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.123-134
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• 2008

In the present article, we give a description of a chain complex of a cyclic cohomology type proposed by Grayson, which is constructed from the double exact sequences of an exact category. We also provide some results which relate it with motivic cohomology of a smooth scheme over a field.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.217-226
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• 2006

In this paper, we investigate the mutual relation among short exact sequences of amalgamated free products which involve augmentation ideals and relation modules. In particular, we find out commutative diagrams having a steady structure in the sense that all of their three columns and rows are short exact sequences.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1215-1231
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• 2023

In this paper, we investigate the nonnil-exact sequences and nonnil-commutative diagrams and show that they behave in a way similar to the classical ones in Abelian categories.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.521-536
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. In this paper, we introduce and study the notions of u-S-pure u-S-exact sequences and uniformly S-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then we characterize uniformly S-von Neumann regular rings and uniformly S-Noetherian rings using uniformly S-absolutely pure modules.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1051-1068
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• 2015

We use methods of relative homological algebra on the category C(mod${\Lambda}$), of complexes of finitely generated modules over an artin algebra ${\Lambda}$, to give some characterizations of almost split sequences.

• Honam Mathematical Journal
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• v.18 no.1
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• pp.91-97
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• 1996

• Journal of KIISE:Databases
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• v.33 no.3
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• pp.251-260
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• 2006

Homology searching on the primary structure (i.e., amino acid arrangement) of protein sequences is an essential part in predicting the functions and evolutionary histories of proteins. However, proteins distant in an evolutionary history do not conserve amino acid residue arrangements, while preserving their structures. Therefore, homology searching on proteins' secondary structure is quite important in finding out distant homology. In this manuscript, we propose an indexing scheme for efficient approximate searching on the secondary structure of protein sequences which can be easily implemented in RDBMS. Exploiting the concept of clustering and lookahead, the proposed indexing scheme processes three types of secondary structure queries (i.e., exact match, range match, and wildcard match) very quickly. To evaluate the performance of the proposed method, we conducted extensive experiments using a set of actual protein sequences. CSI was proved to be faster than the existing indexing methods up to 6.3 times in exact match, 3.3 times in range match, and 1.5 times in wildcard match, respectively.