• Korean Journal of Mathematics
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• v.17 no.2
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• pp.189-196
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• 2009

Let D be an integral domain, and let U be a group of units of D. Let $D^*=D-\{0\}$ and ${\Gamma}=D^*/U$ be the commutative cancellative semigroup under aU+bU=abU. We prove that $Cl(D)=Cl({\Gamma})$ and that D is a PvMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if ${\Gamma}$ is a PvMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let U=U(D) be the group of units of D. We also show that if D is integrally closed, then $D[{\Gamma}]$, the semigroup ring of ${\Gamma}$ over D, is an integrally closed domain with $Cl(D[{\Gamma}])=Cl(D){\oplus}Cl(D)$; hence D is a PvMD (resp., GCD-domain, Krull domain, factorial domain) if and only if $D[{\Gamma}]$ is.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1163-1173
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• 2014

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.97-111
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• 2015

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $c{\in}R$ and $0{\neq}abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

• Bulletin of the Korean Chemical Society
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• v.26 no.4
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• pp.585-588
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• 2005

Bipyridine and its derivatives have been widely used as the ligands in transition metal complexes. The proton affinities of pyridine derivatives were calculated using an ab initio quantum mechanical method (B3LYP with various double zeta and triple zeta basis sets) in combination with the Poisson-Boltzmann continuum solvation model. Van der Waals radii of the atoms in the heterocyclic rings for the solvation energy calculation were set to values determined to reproduce the $pK_a$ values of guanine and oxoguanine derivatives and that of chlorine was optimized to reproduce the experimental values of relating compounds. The $pK_a$ values for the heterocyclic ring compounds were in agreement with the experimental values with a mean unsigned error of 0.45 $pK_a$ units.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.737-742
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• 2014

The vibronic emission spectra of isomeric trimethylbenzyl radicals were reassigned based on substituent effect on electronic transition energy as well as ab initio calculation of the benzyl radical. The electronic transition energy of three isomeric jet-cooled trimethylbenzyl radicals produced by corona discharge of 1,2,3,5-tetramethylbenzene were analyzed using the empirical data of three isomeric methylbenzyl radicals. Calculated data were obtained by summing up the shifts measured from methylbenzyl radicals as well as taking the position and alignment of substituents on the benzene ring into account. The revised assignments show better agreement with observation, and rationalize the validity of the model developed to explain the substituent effect on electronic transition energy of benzyl radicals.

• 한국초전도학회:학술대회논문집
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• 2007.07a
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• pp.31-31
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• 2007

• Bulletin of the Korean Chemical Society
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• v.32 no.1
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• pp.89-94
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• 2011

The mechanism of the cycloaddition reaction of forming germanic bis-heterocyclic compound between singlet dimethylgermylene carbene and acetone has been investigated with CCSD(T)//B3LYP/6-$31G^*$ method. From the potential energy profile, it can be predicted that, this reaction has one dominant channel. The presented rule of this dominant channel is that the two reactants firstly form a four-membered ring carbene (RC4) through the [2+2] cycloaddition reaction. Due to $sp^2$ hybridization of carbene C atom in RC4, RC4 further combines with acetone to form a reactant complexe (RC5). Due to the further $sp^3$ hybridization of carbene C atom in RC4, RC5 isomerizes to a germanic bisheterocyclic compound (P6) via the transition state (TS5).

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.306-307
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• 2006

The sinter-bonding behavior of iron based powder mixtures was investigated. To produce the green compacts to be joined the following powders based on $H{\ddot{o}}gan{\ddot{a}}s$ AB grade NC 100.24 plain iron powder were used: NC 100.24 as delivered, PNC 30, PNC 60 and NC 100.24 + 4%Cu powder mixtures. Dimensional behaviour of all those materials during the sintering cycle was monitored by dilatometry. Simple ring shaped specimens as the outer parts and cylindrical as the inner parts were pressed. The influence of parts' composition on joining strength was established. Diffusion of alloying elements: copper and phosphorous, across the bonding surface was controlled by metallography, SEM and microanalysis.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.195-204
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• 2021

Let R be a G-graded commutative ring with a nonzero unity and P be a proper graded ideal of R. Then P is said to be a graded uniformly pr-ideal of R if there exists n ∈ ℕ such that whenever a, b ∈ h(R) with ab ∈ P and Ann(a) = {0}, then bn ∈ P. The smallest such n is called the order of P and is denoted by ordR(P). In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly pr-ideals in graded factor rings and in direct product of graded rings.