• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.413-422
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• 2021

The Study determinant is known as one of replacements for the determinant of matrices with entries in a noncommutative ring. In this paper, we give a generalization of the Study determinant and show its relationship with the Cayley-Dickson process. We also give some properties of a non-associative ring obtained by the Cayley-Dickson process with a not necessarily commutative, but associative ring as the initial ring.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.331-342
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• 2017

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for $a{\in}Z(R)$, let $ann(a)=\{r{\in}R{\mid}ra=0\}$. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if $ann(xy){\neq}ann(x){\cup}ann(y)$. In this paper, we study the annihilator graph associated to a group ring RG.

• Journal of Sasang Constitutional Medicine
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• v.18 no.3
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• pp.145-154
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• 2006

1. Purpose This study was performed to find the objective Sasang Constitutional Diagnosis, The O-ring test is thought to be one of the several methods to classify constitution. But the O-ring test has several problems. I studied the Sasang Constitutional Diagnosis which is used by Pinch-Guage and Herb Drugs for alternative methods. 2. Methods I tested 89 person's grasping power with changing the medical herb which is exist on person's another hand. conclusion of the test was compared with that of QSCC II to confirm the significance of this study. 3. Results and conclusions Soyangin group, Taeumin group, Male Soyangin goup, Male Taeumin group and Male group have a significant result on converting grades statistically.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.274-279
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• 1992

Immobilization method of lariat azacrown ethers, containing hydroxyl group in the side arm of crown ring, on the polymer matrix and the phase-transfer catalytic activity of thus obtained immobilized lariat azacrown ethers were studied. Polystyrene resins with crown ether structures and hydroxyl groups adjacent to the macrorings were prepared by the reaction of crosslinked polystyrene resins containing epoxy groups with monoaza-15-crown-5 or monoaza-18-crown-6. Microporous crosslinked polystyrene resins containing epoxy group for the syntheses of these immobilized lariat crown catalysts were prepared by suspension polymerization of styrene, divinylbenzene (DVB 2%) and vinylbenzylglycidyl ether. The immobilized lariat catalysts with 10-20% ring substitution exhibited maximal activity for the halogen exchange reactions of 1-bromooctane with aqueous KI or NaI under triphase heterogeneous conditions. Immobilized catalyst exhibited higher activity than corresponding catalyst without the hydroxyl group and this result was suggested that the active site have a structure in which the $K^+$ ion was bound by the cooperative coordination of the crown ring donors and the hydroxyl group in the side arm.

• Applied Biological Chemistry
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• v.41 no.1
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• pp.99-103
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• 1998

Triazolopyrimidine sulfonanilide (TP) derivative is one of excellent herbicide compounds. We have synthesized three classes of a new sulfonamide derivative (TPP) as Acetolactate synthase (ALS) inhibitors, in which the benzene ring in TP skeleton was converted to substituted pyrimidyl ring and examined their inhibitory activities on barley for ALS. $I_{50}$ values of the inhibitors ranged from 0.005 to 2 mM. Comparing the $I_{50}$ value of each class of TPP derivatives, the substituents in pyrimidine and triazolopyrimidine ring were found to affect the degree of ALS inhibition. TPP with substituted methyl group in pyrimidine ring showed higher inhibitory activity than that with methoxy group, while the substitution of the cyclopentano group in triazolopyrimidine ring gave very large inhibitory activity than that of methyl group. The present study established that variation of the electron density by substitution at heterocyclic ring is a very important factor for ALS inhibition, but showed no dependence on steric effect by substituents.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.599-620
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• 2005

There can be two different approaches to introducing Abstract Algebra to undergraduate students: One is to introduce group concept prior to ring concept, and the other is to do the other way around. Although the former is almost conventional, it is worth while to take the latter into consideration in the viewpoint that students are already familiar to rings of integers and polynomials. In this paper, we investigated 16 most commonly used Abstract Algebra undergraduate textbooks and found that 5 of them introduce ring theory prior to group theory while the rest do the other way around. In addition, we interviewed several undergraduate students who already have taken an Abstract Algebra course to look into which approach they prefer. Then we compare pros and cons of two approaches on the basis of the results of the interview and the historico-genetic principle of teaching and learning in Abstract Algebra and suggest that it certainly be one of alternatives to introduce ring theory before group theory in its standpoint.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1647-1659
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• 2008

Let R be a ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. First, we investigate some connected conditions of the zero-divisor graph $\Gamma(R)$ of a noncommutative ring R as follows: (1) if $\Gamma(R)$ has no sources and no sinks, then $\Gamma(R)$ is connected and diameter of $\Gamma(R)$, denoted by diam($\Gamma(R)$) (resp. girth of $\Gamma(R)$, denoted by g($\Gamma(R)$)) is equal to or less than 3; (2) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3, in addition, if R is local, then there is a vertex of $\Gamma(R)$ which is adjacent to every other vertices in $\Gamma(R)$; (3) if R is unit-regular, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3. Next, we investigate the graph automorphisms group of $\Gamma(Mat_2(\mathbb{Z}_p))$ where $Mat_2(\mathbb{Z}_p)$ is the ring of 2 by 2 matrices over the galois field $\mathbb{Z}_p$ (p is any prime).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39B no.9
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• pp.555-560
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• 2014

Recently, there are many researches on sharing group session key for members in a group. Among them, Harn and Lin proposed a scheme based on the Shamir's group session key and Liu, Cheng, Cao, and Jiang improved it to reduce the specific weakness. Especially, these schemes are based on the finite integer ring to protest the insider attack, in which a valid member can derived another member's secret using known information. In this paper, it is shown that the finite integer ring implies the failure of the reconstruction of group session key depending on the adopted parameters. We fix this problem and propose new group session key transfer scheme using the Shamir's secret sharing.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1629-1643
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• 2016

Let R be a ring with identity, X be the set of all nonzero, nonunits of R and G be the group of all units of R. A ring R is called unit-duo ring if $[x]_{\ell}=[x]_r$ for all $x{\in}X$ where $[x]_{\ell}=\{ux{\mid}u{\in}G\}$ (resp. $[x]_r=\{xu{\mid}u{\in}G\}$) which are equivalence classes on X. It is shown that for a semisimple unit-duo ring R (for example, a strongly regular ring), there exist a finite number of equivalence classes on X if and only if R is artinian. By considering the zero divisor graph (denoted ${\tilde{\Gamma}}(R)$) determined by equivalence classes of zero divisors of a unit-duo ring R, it is shown that for a unit-duo ring R such that ${\tilde{\Gamma}}(R)$ is a finite graph, R is local if and only if diam(${\tilde{\Gamma}}(R)$) = 2.

• 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.