• Honam Mathematical Journal
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• v.28 no.3
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• pp.377-386
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• 2006

For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, $ann_R(a)$, for each $a{\in}R$ is a pure ideal in R. Also it is proved that the polynomial ring, R[x], is a PF-ring if and only if R is a PF-ring. Finally, we prove that M as an R-module is PF-module if and only if M[x] is a PF R[x]-module. Also M is a PP R-module if and only if M[x] is a PP R[x]-module.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1289-1304
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• 2022

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

• Journal of the Microelectronics and Packaging Society
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• v.8 no.1
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• pp.19-25
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• 2001

In this paper, the design and simulation results of IF frequency synthesizer section has been described. We has been used 0.8 $\mu\textrm{m}$ BiCMOS device and library of the AMS. IF frequency synthesizer section has been contained IF VCO, Phase Detector, Divide_by_8, Charge Pump and Loop Filter. IF frequency synthesizer has been shown operating voltage of 2.7~3.6 V, control voltage of 0.5~2.7 V and supply current of 11 mA. The measured results have been showed good agreement with the simulation results about supply current.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.135-146
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• 2009

In the present note we study the properties of weak Armendariz rings, and the connections among weak Armendariz rings, Armendariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a finite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is infinite dimensional, from given any semi prime ring. We next find more examples of weak Armendariz rings.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.487-494
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• 2021

In this paper, we study rings with Noetherian spectrum, rings with locally Noetherian spectrum and rings with t-locally Noetherian spectrum in terms of the polynomial ring, the Serre's conjecture ring, the Nagata ring and the t-Nagata ring. In fact, we show that a commutative ring R with identity has Noetherian spectrum if and only if the Serre's conjecture ring R[X]_U has Noetherian spectrum, if and only if the Nagata ring R[X]_N has Noetherian spectrum. We also prove that an integral domain D has locally Noetherian spectrum if and only if the Nagata ring D[X]_N has locally Noetherian spectrum. Finally, we show that an integral domain D has t-locally Noetherian spectrum if and only if the polynomial ring D[X] has t-locally Noetherian spectrum, if and only if the t-Nagata ring $D[X]_{N_v}$ has (t-)locally Noetherian spectrum.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1039-1052
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• 2021

In this paper, we introduce and study the class of 𝜙-w-flat modules which are generalizations of both 𝜙-flat modules and w-flat modules. The 𝜙-w-weak global dimension 𝜙-w-w.gl.dim(R) of a commutative ring R is also introduced and studied. We show that, for a 𝜙-ring R, 𝜙-w-w.gl.dim(R) = 0 if and only if w-dim(R) = 0 if and only if R is a 𝜙-von Neumann ring. It is also proved that, for a strongly 𝜙-ring R, 𝜙-w-w.gl.dim(R) ≤ 1 if and only if each nonnil ideal of R is 𝜙-w-flat, if and only if R is a 𝜙-PvMR, if and only if R is a PvMR.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1051-1066
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• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Journal of Microbiology and Biotechnology
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• v.11 no.6
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• pp.986-993
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• 2001

Translation Initiation in prokaryotes involves the formation of a 30 S preinitiation complex, in which translation initiation factors play a role in the stimulation of fMet-tRNA (fMet) binding. However, the specific function and precise mechanism of initiation factor IF1 are still unclear. One a functionally active factor with a high purity. In the present study a large quantity of active IF was rapidly purified, obtained by the overexpression of the infA gene, and then used for a functional study. The induction of infA did not appreciably affect the growth rate of the protease-deficient strain E. coli AR68 harboring the IF1 overproducing plasmid. The level of IF1 obtained was approximately $1-2\%$ of the total cell protein, which enabled the yield of highly purified IF1 (>$98\%$ pure) to be increased to 0.15 mg of IF1/g of cells. The IF1 was isolated within one day by the centrifugatioin of the ribosomal washed fraction, by ammonium sulfate fractionation, chromatography on batch of phosphocellulose, and FPLC Mono S. The overexpressed IF1 was found to be comparable to the factor isolated from normal cells, as determined by migration in NEPHGE/SDS 2-D gels. For binding of fMet-tRNA(fMet) to the 30 S ribosomal subunitis, relatively high levels of binding were obtained when IF2 was present. The addition of IF1 up to 110 pmol proportionally stimulated the binding to a variable extent. This IF1-dependent stimulation of the 30 S preinitiation complex formation demonstrated that IF1 would appear to be exclusively essential for promoting the initiation phase of protein synthesis.

• Korean Journal of Microbiology
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• v.40 no.1
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• pp.7-11
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• 2004

eIF5B is a translation initiation factor that delivers Met-$tRNA^{Met}$ to AUG start codon and subsequently joins the small and large ribosomes. In order to study the function of eIF5B encoded by FUN12, we constructed FUN12 which lacked 5' end of its sequence. We found that this construct lacking almost all of its promoter in pRS plasmid partially complemented slow growth phenotype of fun12 deletion strain. Interestingly, this construct expressed N-terminally truncated eIF5B and its expression level was about 5% of that of wild type eIF5B. Low amount of the eIF5B expressed additionally in fun12 deletion strain played a direct role as a limiting factor for its growth. This limiting factor eIF5B in those strains also modulates activities of overall translation in vitro.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.