• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.331-336
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• 2007

We consider infinite nested radicals in which the arguments are positive polynomial sequences. It is shown that the evaluation of such a nesting is always finite, and we prove necessary and sufficient conditions for the evaluation to be a finite polynomial.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.687-691
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• 2010

In this article we will prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index, respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek in [5].

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1511-1528
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• 2020

A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.

• Journal of the Korean Chemical Society
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• v.14 no.3
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• pp.207-212
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• 1970

A large variety of weed killers, insecticides, and bactericiedes on the market today are of almost infinite variety, but their pharmacological effects are different from each other according to the objects to cope with. Therefore, it is hoped that some chemical substance which serves as weed killer, an insecticide, and a bactericede at a same time, should be synthesized, in order to save expense and labor. I anticipated that the desire would be met by introducing to a molecule the radical which has the three effects. Here, I made an attempt of introducing $Cl_2$ gas to aniline considering the following respects: 1. Introduction velocity of $Cl_2$ gas under the varied temeratures and velocities of $Cl_2$ gas 2. The effect of reaction period under the condition which gives the most satisfactory yield. 3. The actions of catalysts, $SbCl_3$, $FeCl_3$, and $MoCl_5$, and their proportions when a mixture of the three catalysts is used in producing 2,6-dichloro-aniline. After consideration of above phenomena, the maximum production rate of 79.5% of 2.6-compound was obtained. With the compound I synthesized 2.6-dichloro-4-nitroaniline-mercuric acetate. Investigations of the effects of the compound as weed killer, an insecticide, and a bactericide showed that the compound, 2,6-dichloro-4-Nitro Aniline mercuric acetate has a satisfactory herbi-insecti-bactericidal effect.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1233-1254
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• 2023

We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.