• 대한수학회보
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• 제59권6호
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Kyungpook Mathematical Journal
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• 제51권3호
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• pp.301-309
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• 2011

In this paper we dene the notions of left *-bimultiplier, *-bimultiplier and generalized *-biderivation, and to prove that if a semiprime *-ring admits a left *-bimultiplier M, then M maps R ${\times}$ R into Z(R). In Section 3, we discuss the applications of theory of *-bimultipliers. Further, it was shown that if a semiprime *-ring R admits a symmetric generalized *-biderivation G : R ${\times}$ R ${\rightarrow}$ R with an associated nonzero symmetric *-biderivation R ${\times}$ R ${\rightarrow}$ R, then G maps R ${\times}$ R into Z(R). As an application, we establish corresponding results in the setting of $C^*$-algebra.

• 수산해양교육연구
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• 제28권1호
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• pp.59-68
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• 2016

For comparison of tetracycline-resistant ($Tc^R$) genes, we obtained 21 and 14 $Tc^R$ Staphylococcus spp. from marine environment and human patient, respectively. Although all isolates from human were identified as Staphylococcus aureus, higher proportion of $Tc^R$ isolates (12 out of 14) from human were utilizing tet(M) gene compared to that of $Tc^R$ isolates (6 out of 21) from marine environment. Additionally, collaborated utilization of tet(M) and erm(A) in $Tc^R-Em^R$ S. aureus in human patient, but not in $Tc^R$ Staphylococcus spp. isolates from marine environment was also characterized. Based on the nucleotide sequence of transposon related to $Tc^R$ gene, we confirmed the origin of tet(M) gene in $Tc^R$ Staphylococci isolated from marine environments and human are derived from Tn916/1545-like and Tn5801 transposon, respectively. It is the first report showing the presence of Tn5801 in all $Tc^R$ S. aureus carrying tet(M) in human patient. Alignment of the fully sequenced tet(M) from marine environmental isolates was also agreed with the determined transposons by showing the genomic mosaic structure composed with three genomic parts from Tn916/1545 and unknown transposons. Genetic characteristics of these tet(M) in environmental isolates were similar to each other but different from those in isolates from human showing only tet(M) from Tn916/5801 type. It may imply the presence of less dramatic communication of antibiotic resistant genes between Staphylococci isolated from marine environment and human.

• 대한수학회보
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• 제52권4호
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• pp.1365-1373
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• 2015

We find all ${\mathcal{F}}{\mathcal{M}}_m$-natural operators A transforming torsion free classical linear connections ${\nabla}$ on m-manifolds M into base preserving fibred maps $A({\nabla}):{\bar{J}}^rY{\rightarrow}J^rY$ for ${\mathcal{F}}{\mathcal{M}}_m$-objects Y with bases M, where ${\bar{J}}^r$, $J^r$ are the semiholonomic and holonomic jet functors of order r on the category ${\mathcal{F}}{\mathcal{M}}_m$ of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps.

• 대한수학회보
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• 제41권3호
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• pp.419-426
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• 2004

Let R be a commutative Noetherian ring and let M be an Artinian R-module. Let M${\subseteq}$M′ be submodules of M. Suppose F is an R-module which is projective relative to M. Then it is shown that $Att_{R}$($Hom_{A}$ (F,M′) :$Hom_{A}$(F,M) $In^n$), n ${\in}$N and $Att_{R}$($Hom_{A}$(F,M′) :$Hom_{A}$(F,M) In$^n$ $Hom_{A}$(F,M") :$Hom_{A}$(F,M) $In^n$),n ${\in}$ N are ultimately constant.

• 대한수학회보
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• 제54권1호
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• pp.319-329
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• 2017

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• 대한수학회논문집
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• 제22권1호
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• pp.41-51
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• 2007

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

• 대한기계학회논문집B
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• 제20권2호
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• pp.730-740
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• 1996

Boiling heat transfer coefficients of pure refrigerants (R22, R32, R134a, R125, R290, and R600a) and refrigerant mixtures (R32/Rl34a, R290/ R600a, and R32/R125) are measured experimentally and compared with Chen's correlation. The test section is a seamless stainless steel tube with inner diameter of 7.7mm and uniformly heated by applying electric current directly to the tube. Heat fluxes range from 10 to 30kW$^2$. Mass fluxes are set to 424 ~ 742kg/m$^{2}$s for R22, R32, R134a, R32/R134a, and R32/Rl25 ; 265 ~ 583kg/m$^{2}$s for R290, R600a, and R290/R600a. Heat transfer coefficients depend strongly on heat flux at a low quality region and become independent as quality increases. Convective boiling term in the Chen's correlation predicts experimental data of the pure refrigerants fairly well (relative error of 12.1% for the data of quality over 0.2). The correlation for pure substances overpredicts the heat transfer coefficients for nonazeotropic refrigerant mixtures.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.93-96
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• 1997

An atomic integral domain R is a half-factorial domain (HFD) if whenever $\chi_1$… $\chi_{m}=y_1$…$y_n$ with each $\chi_{i},y_j \in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then $Cl_{t}(R)$ $\cong$ $Cl_{t}$(R[X]), and if $G_1$ and $G_2$ are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = $G_1\bigoplus\; G_2$.

• 한국농림기상학회:학술대회논문집
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• 한국농림기상학회 2016년도 추계 학술발표논문집
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• pp.111-117
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• 2016