• 대한수학회논문집
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• 제35권2호
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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.

• 대한수학회보
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• 제42권1호
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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.

• 대한수학회논문집
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• 제38권1호
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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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• 제16권2호
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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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• 제14권2호
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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.

• 대한수학회지
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• 제60권6호
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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.

• 대한수학회지
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• 제60권3호
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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.

• 대한수학회지
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• 제52권5호
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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.

• 호남수학학술지
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• 제18권1호
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• pp.91-97
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• 1996

• 한국정보과학회논문지:데이타베이스
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• 제33권3호
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• pp.251-260
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• 2006

단백질 일차 구조(아미노산 배열)에 대한 상동 검색은 유전자나 단백질의 기능과 진화 과정을 유추하기 위한 필수 연산이다. 그러나 진화 단계가 멀리 떨어진 경우 단백질 일차 구조는 보존되지 않기 때문에 단백질의 공간적 구조에 대한 유사 검색을 통해서만 진화 단계를 유추할 수 있다. 따라서 본 논문에서는 단백질의 공간적 구조를 표현하는 단백질 이차 구조를 대상으로 하여 RDBMS상에 쉽게 구현이 가능한 인덱싱 방안을 제안한다. 제안된 인덱싱 방안은 클러스터링 기법과 LookAhead 개념을 활용하여 Exact Match, Range Match, Wildcard Match 질의를 신속하게 처리한다. 제안된 방법의 우수성을 검증하기 위하여 실제의 단백질 데이타를 대상으로 성능 평가를 수행하였다. 실험 결과에 의하면, 제안된 방법은 기존의 방법과 비교하여 Exact Match의 경우 6.3배까지, Range Match의 경우 3.3배까지, Wildcard Match의 경우 1.5배까지의 개선된 검색 성능을 가지는 것으로 나타났다.