• 대한수학회논문집
• /
• 제36권3호
• /
• pp.413-422
• /
• 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.

• 대한수학회보
• /
• 제54권1호
• /
• pp.331-342
• /
• 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.

• 사상체질의학회지
• /
• 제18권3호
• /
• pp.145-154
• /
• 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
• /
• 제13권3호
• /
• pp.274-279
• /
• 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
• /
• 제41권1호
• /
• pp.99-103
• /
• 1998

Triazolopyrimidine sulfonanilide (TP) 유도체는 널리 사용되고 있는 제초제 중의 하나이다. 우리는 TP 유도체 화합물의 골격을 이루고 있는 벤젠 고리를 pyrimidine 고리로 치환시킨 새로운 3 종류의 sulfonamide 유도체(TPP)를 합성하고, 보리에서 추출한 acetolactate synthase (ALS)의 저해 활성도를 측정한 결과 0.005 부터 2 mM 사이의$I_{50}$값을 얻었다. $I_{50}$ 값의 비교에서 pyrimidine 고리에 methyl기가 치환된 TPP 유도체는 methoxy기가 치환된 유도체 보다 높은 저해 활성도를 나타내었다. 또한 triazolopyrimidine 고리에 cyclopentano 고리로 치환된 TPP 유도체는 methyl- 및 phenyl가 치환된 유도체보다 우수한 저해 활성도를 보였다. 따라서 새로운 TPP 유도체의 제초 효력은 치환기에 의한 분자내 전자 분포 변화와 밀접한 관계가 있으나 치환기의 크기에 따른 입체적 장애 요인은 저해 활성도에 전혀 영향이 없음을 알 수 있었다.

• 한국수학교육학회지시리즈E:수학교육논문집
• /
• 제19권4호
• /
• pp.599-620
• /
• 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.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1647-1659
• /
• 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).

• 한국통신학회논문지
• /
• 제39B권9호
• /
• pp.555-560
• /
• 2014

최근 그룹 내의 여러 멤버 사이에 하나의 그룹 세션키를 공유하는 연구가 활발히 진행되고 있다. 그 중에서 Harn과 Lin에 의해 Shamir의 비밀 공유 방식을 이용한 방식이 제안되었고, 이를 개선한 프로토콜이 Liu, Cheng, Cao, 그리고 Jiang에 의해서 다시 제안되었다. 특히 기존 방식들에서는 특정한 일부 비밀 정보를 알고 있는 그룹 멤버에 의해 다른 비밀 값이 알려지게 되는 '내부자 공격'에 대응하기 위해 유한한 원소를 갖는 유한 정수 환(finite integer ring)상에서 연산이 이루어지도록 프로토콜을 설계하였다. 이 논문에서는 기존 방식들이 기반을 둔 유한 정수 환상의 그룹 세션키 분배 연산에서는 정당한 그룹 멤버들도 특정한 조건에서는 키 복구가 불가능한 상황이 발생하여 그룹 키 전송이 실패할 수 있음을 먼저 밝힐 것이다. 또한 이런 문제를 해결할 수 있는 새로운 프로토콜을 설계하여 제안한다.

• 대한수학회보
• /
• 제53권6호
• /
• pp.1629-1643
• /
• 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.

• 대한수학회보
• /
• 제57권6호
• /
• pp.1511-1528
• /
• 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.