• 대한수학회지
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• 제58권6호
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• 대한수학회지
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• 제58권2호
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• 호남수학학술지
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• 제45권3호
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• pp.410-417
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• 2023

Suppose that there are 8 abelian varieties defined over a number field K which satisfy a commutative diagram. We show that if we know that three out of four short exact sequences satisfy the rate formula of Tate-Shafarevich groups, then the unknown short exact sequence satisfies the rate formula of Tate-Shafarevich groups, too.

• 호남수학학술지
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• 제34권3호
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• pp.423-438
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• 2012

In this paper, we discuss numbers of downwards and upwards in generalized paper folding sequences. We compute the exact number of downwards and upwards in $R^n_p$ and $(R_pR_q)^n$ by using the properties of recursive sequences where n, p and q are natural numbers with $p{\geq}2$ and $q{\geq}2$.

• 대한수학회지
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• 제27권2호
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• pp.177-184
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• 1990

• Kyungpook Mathematical Journal
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• 제19권2호
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• pp.223-230
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• 1979

• 대한수학회보
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• 제43권1호
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• pp.225-225
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• 2006

In this note a modification of Proposition 3.10 of [1] is given.

• 한국산업정보학회논문지
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• 제17권6호
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• pp.41-50
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• 2012

This paper presents a new sequence alignment method using the divide approach, which solves the problem by decomposing sequence alignment into several sub-alignments with respect to exact matching subsequences. Exact matching subsequences in the proposed method are bounded on the generalized suffix tree of two sequences, such as protein domain length more than 7 and less than 7. Experiment results show that protein sequence pairs chosen in PFAM database can be aligned using this method. In addition, this method reduces the time about 15% and space of the conventional dynamic programming approach. And the sequences were classified with 94% of accuracy.

• 대한수학회논문집
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• 제17권4호
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• pp.693-708
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• 2002

We generalize algebraic results of Nielsen fixed point theory to Nielsen coincidence theory. We use the algebraic methods of D. Ferrario in Nielsen fixed point theory.

• 한국지능시스템학회논문지
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• 제15권4호
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• pp.511-513
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• 2005

We investigate some situations in connection with two exact sequences of fuzzy linear maps.