• Korean Journal of Mathematics
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• v.24 no.3
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• pp.307-317
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• 2016

Let R be a ring. It is well-known that R is NI if and only if ${\sum}^n_{i=0}Ra_i$ is a nil ideal of R whenever a polynomial ${\sum}^n_{i=0}a_ix^i$ is nilpotent, where x is an indeterminate over R. We consider a condition which is similar to the preceding one: ${\sum}^n_{i=0}Ra_iR$ contains a nonzero nil ideal of R whenever ${\sum}^n_{i=0}a_ix^i$ over R is nilpotent. A ring will be said to be quasi-NI if it satises this condition. The structure of quasi-NI rings is observed, and various examples are given to situations which raised naturally in the process.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1193-1205
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• 2018

We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be NJ if it satisfies such property. We prove the following: (i) $K{\ddot{o}}the^{\prime}s$ conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If R is an NJ ring, then R is exchange if and only if it is clean; and (iii) A ring R is NJ if and only if so is every (one-sided) corner ring of R.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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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.

• East Asian mathematical journal
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• v.34 no.1
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• pp.39-46
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• 2018

In this article we consider rings whose Jacobson radical contains all the nilpotent elements, and call such a ring an NJ-ring. The class of NJ-rings contains NI-rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.279-288
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• 2014

The studies of reversible and 2-primal rings have done important roles in noncommutative ring theory. We in this note introduce the concept of quasi-reversible-over-prime-radical (simply, QRPR) as a generalization of the 2-primal ring property. A ring is called QRPR if ab = 0 for $a,b{\in}R$ implies that ab is contained in the prime radical. In this note we study the structure of QRPR rings and examine the QRPR property of several kinds of ring extensions which have roles in noncommutative ring theory.

• Bulletin of the Korean Chemical Society
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• v.17 no.2
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• pp.173-179
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• 1996

A series of tetradentate Schiff base ligands; [1,2-bis(naphthylideneimino)ethane, 1,3-bis(naphthylideneimino)propane, 1,4-bis(naphthylideneimino)butane, and 1,5-bis(naphthylideneimino)pentane] and their Ni(Ⅱ) complexes have been synthesized. The properties of these ligands and their Ni(Ⅱ) complexes have been characterized by elemental analysis, IR, NMR, UV-vis spectra, molar conductance, and thermogravimetric analysis. The mole ratio of Schiff base to Ni(Ⅱ) metal was found to be 1:1. The electrochemical redox process of the ligands and their Ni(Ⅱ) complexes in DMF and DMSO solution containing 0.1 M tetraethyl ammonium perchlorate (TEAP) as a supporting electrolyte have been investigated by cyclic voltammetry, chronoamperometry, differential pulse voltammetry, and controlled potential coulometry at glassy carbon electrode. The redox process of the ligands was highly irreversible, whereas redox process of Ni(Ⅱ) complexes were observed as one electron transfer process in quasi-reversible and diffusion-controlled reaction. The electrochemical redox potentials of the Ni(Ⅱ) complexes were affected by the chelate ring size of ligands. The diffusion coefficients of Ni(Ⅱ) complexes containing 0.1 M TEAP in DMSO solution were determined to be 5.7-6.9 × 10-6 cm2/sec. Also the exchange rate constants were determined to be 1.8-9.5 × 10-2 cm2/sec. These values were affected by the chelate ring size of ligands.

• Bulletin of the Korean Chemical Society
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• v.28 no.11
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• pp.1996-2002
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• 2007

The redox behavior of a [Ni6(μ3-Se)2(μ4-Se)3(Fe(η 5-C5H4P-Ph2)2)3] (= [Ni-Se-dppf], dppf = 1,1-bis(diphenylphosphino) ferrocene) cluster was studied using platinum (Pt) and glassy carbon electrodes (GCE) in nonaqueous media. The cluster showed electrochemical activity at the potential range between +1.6 and ?1.6 V. In the negative region (0 to ?1.6 V), the cluster exhibited two-step reductions. The first step was one-electron reversible, while the second step was a five-electron quasi-reversible process. On the other hand, in the positive region (0 to +1.6 V), the first step involved one-electron quasi-reversible process. The applicability of the cluster was found towards the electrocatalytic reduction of CO2 and was evaluated by experiments using rotating ring disc electrode (RRDE). RRDE experiments demonstrated that two electrons were involved in the electrocatalytic reduction of CO2 to CO at the Se-Ni-dppf-modified electrode.

• Bulletin of the Korean Chemical Society
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• v.18 no.8
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• pp.850-856
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• 1997

A series of tetradentate Schiff-base ligands; 1,3-bis(salicylideneimino) propane, 1,4-bis(salicylideneimino)butane, and 1,5-bis(salicylideneimino)pentane, and their Cu(Ⅱ) and Ni(Ⅱ) complexes have been synthesized. The properties of ligands and complexes have been characterized by elemental analysis, IR, NMR, UV-Vis spectra, molar conductance, and thermogravimetric anaylsis. The mole ratio of Schiff base to metal at complexes was found to be 1 : 1. All complexes were four-coordinated configuration and non-ionic compound. The electrochemical redox processes of the ligands and their complexes in DMF solution containing 0.1 M TEAP as supporting electrolyte have been investigated by cyclic voltammetry, chronoamperometry, differential pulse voltammetry at glassy carbon electrode, and by controlled potential coulometry at platinum gauze electrode. The redox process of the ligands was highly irreversible, whereas redox process of Cu(Ⅱ) and Ni(Ⅱ) complexes was observed as one electron transfer process of quasi-reversible and diffusion-controlled reaction. Also the electrochemical redox potentials of complexes were affected by chelate ring size of ligands. The diffusion coefficients of Cu(Ⅱ) and Ni(Ⅱ) complexes in DMF solution were determined to be 4.2-6.6×10-6 cm2/sec. Also the exchange rate constants were determined to be 3.6-9.7×10-2 cm/sec.