• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.71-72
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• 2020

A ring R is quasi-reversible if 0 ≠ ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].

• 대한수학회논문집
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• 제36권2호
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• pp.209-227
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• 2021

In this paper, we deal with the question that what kind of properties does a ring gain when it satisfies symmetricity or reversibility by the way of nilpotent elements? By the motivation of this question, we approach to symmetric and reversible property of rings via nilpotents. For symmetricity, we call a ring R middle right-(resp. left-)nil symmetric (mr-nil (resp. ml-nil) symmetric, for short) if abc = 0 implies acb = 0 (resp. bac = 0) for a, c ∈ R and b ∈ nil(R) where nil(R) is the set of all nilpotent elements of R. It is proved that mr-nil symmetric rings are abelian and so directly finite. We show that the class of mr-nil symmetric rings strictly lies between the classes of symmetric rings and weak right nil-symmetric rings. For reversibility, we introduce left (resp. right) N-reversible ideal I of a ring R if for any a ∈ nil(R), b ∈ R, being ab ∈ I implies ba ∈ I (resp. b ∈ nil(R), a ∈ R, being ab ∈ I implies ba ∈ I). A ring R is called left (resp. right) N-reversible if the zero ideal is left (resp. right) N-reversible. Left N-reversibility is a generalization of mr-nil symmetricity. We exactly determine the place of the class of left N-reversible rings which is placed between the classes of reversible rings and CNZ rings. We also obtain that every left N-reversible ring is nil-Armendariz. It is observed that the polynomial ring over a left N-reversible Armendariz ring is also left N-reversible.

• Bulletin of the Korean Chemical Society
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• 제23권2호
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• pp.241-244
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• 2002

Using ab initio method, we have studied the structural stabilities, the electronic structures and properties between the two isomers with $C_{2h}$ and $C_{2v}$ symmetry of AlN four-membered-ring single precursors $[Me_2AlNHR]_2$ (R = Me, $^iPr$, and $^iBu$). In the viewpoint of bond lengths in optimized structures, the N-C bonds are considerably affected by the change of the R groups bonded to nitrogen, but the bonding characters of the Al-N and Al-C bonds are little affected. Also the structural stabilities between the two isomers with $C_{2h}$ and $C_{2v}$ symmetry by using Hartree-Fock (HF) and the second order Moeller-Pleset (MP2) calculations agree well with the experimental results for the relative stability of bis(dimethyl- m-isopropylamido-aluminum) (BDPA) and bis(dimethyl- m-t-butylamido-aluminum) (BDBA), while the semiempirical AM1 and PM3 calculations for BDPA were reverse. Thus, our results may aid in designing an optimum precursor for a given process by explaining the experimental results through the elimination of the R groups bonded to nitrogen.

• Bulletin of the Korean Chemical Society
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• 제24권6호
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• pp.731-732
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• 2003

Mutagen X (MX), 3-chloro-4-(dichloromethyl)-5-hydroxy-2(5H)-furanone is one of the most potent directing acting mutagen ever tested in SAL TA100 assay. Although MX analogues have been synthesized, tested for mutagenicity and modeled by structure-activity relationship (SAR) methods, the mechanism of interaction of these compounds with DNA to produce their remarkable mutagenic potency remains unresolved. MX exists as an equilibrium mixture of both ring and open form in water. This equilibrium is very fast for Ames test. Because the mixture is not separable by experimental methods, it is not clear which one is really responsible for the observed mutagenicity. There have been many debates that which one is really responsible for the observed mutagenicity. We used ab initio methods for the MX analogues. It seems both ring and open form could react with DNA bases as electrophiles. However, every open form has consistently lower LUMO energy than corresponding ring form. It is reasonable to assume that the major reaction will go through via open form for MX analogues. This suggest that the open form is more likely really mutagenic.

• 대한화학회지
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• 제42권1호
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• pp.1-8
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• 1998

티아졸 고리를 포함하는 lexitroposin에서, DNA minor groove의 염기쌍과 결합하는 부분인 티아졸의 분자정전기전위를 ab initio계산을 통해 구하였으며 protonate된 티아졸의 두 가지 가능한 형태에 대해 MNDO 및 ab initio방법으로 기하학적 구조를 최적화 하였다. 최적화된 구조에 대해 6-31G및 6-31G* basis set을 사용하여 양성자 친화도를 구하였으며 아울러 티아졸의 양성자 친화도에 미치는 치환기 효과를 알아보기 위해 전자를 주는 기와 전자를 끄는 기를 치환시킨 여러 치환 치아졸에 대해 양성자 친화도를 조사하였다. 그 결과 티아졸의 질소 원자가 DNA minor groove 쪽으로 배향되고 전자를 주는 기가 치환될 때 양성자 친화도가 증가됨을 알 수 있었다.

• 대한수학회논문집
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• 제31권2호
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• pp.237-246
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• 2016

The purpose of this paper is to introduce some new class of rings that are closely related to the classes of sharp domains, pseudo-Dededkind domains, TV domains and finite character domains. A ring R is called a ${\phi}$-sharp ring if whenever for nonnil ideals I, A, B of R with $I{\supseteq}AB$, then I = A'B' for nonnil ideals A', B' of R where $A^{\prime}{\supseteq}A$ and $B^{\prime}{\supseteq}B$. We proof that a ${\phi}$-Dedekind ring is a ${\phi}$-sharp ring and we get some properties that by them a ${\phi}$-sharp ring is a ${\phi}$-Dedekind ring.

• 대한수학회논문집
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• 제35권2호
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• pp.447-454
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• 2020

The studies of reversible and NI rings have done important roles in noncommutative ring theory. A ring R shall be called QRUR if ab = 0 for a, b ∈ R implies that ba is contained in the upper nilradical of R, which is a generalization of the NI ring property. In this article we investigate the structure of QRUR rings and examine the QRUR property of several kinds of ring extensions including matrix rings and polynomial rings. We also show that if there exists a weakly semicommutative ring but not QRUR, then Köthe's conjecture does not hold.

• East Asian mathematical journal
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• 제37권1호
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• pp.33-40
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• 2021

We discuss the condition that if ab = 0 for elements a, b in a ring R then aIb = 0 for some essential ideal I of R. A ring with such condition is called IEIP. We prove that a ring R is IEIP if and only if Dn(R) is IEIP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. We construct an IEIP ring that is not Abelian and show that a well-known Abelian ring is not IEIP, noting that rings with the insertion-of-factors-property are Abelian.

• Journal of Photoscience
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• 제7권2호
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• pp.67-71
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• 2000

A quantum-chemical investigation on the conformations and electronic properties of trans(diphenyl-diheterocyclic) ethenes(t-PHEs) as building block for fully $\pi$-conjuated polymer are performed in order to display the effects of heterocyclic ring substitution. Structures for the molecules, t-PHEs were fully optimized by using semiempirical AM1, PM3 methods, and ab initio HF methods, with 6-31G basic set. The potential energy curves with respect to the change of single are obtained by using ab initio HF/6-31G basic set. The curves are not similar shapes in the molecules with respect to heterocyclic rings. It is shown that the steric repulsion interactions between phenyl ring and heterocyclic ring are subjected to different type with the respect to each heterocyclic ring. Electronic properties of the molecules were molecules were obtained by applying the optimized structures and selected geometries to the extended Huckel method. To investigate the change of HOMO-LUMO gap with respedt to the torsion angle, we select the optimized structures. By using the results, the dependency of conjugation for the energy gaps is analyzed. For t-PHE the energy gap increase up to 0.52 eV compared with its planar structure. In the cases of t-PHE and t-PHE, the energy gap increase by 1.29 and 1.15 eV, respectively, compared with its planar structure.

• 대한수학회보
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• 제56권4호
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• pp.993-1006
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• 2019

This article concerns a ring property which preserves the reversibility of elements at nonzero idempotents. A ring R shall be said to be quasi-reversible if $0{\neq}ab{\in}I(R)$ for a, $b{\in}R$ implies $ba{\in}I(R)$, where I(R) is the set of all idempotents in R. We investigate the quasi-reversibility of 2 by 2 full and upper triangular matrix rings over various kinds of reversible rings, concluding that the quasi-reversibility is a proper generalization of the reversibility. It is shown that the quasi-reversibility does not pass to polynomial rings. The structure of Abelian rings is also observed in relation with reversibility and quasi-reversibility.