• East Asian mathematical journal
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• 제19권1호
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• pp.151-164
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• 2003

Throughout this paper, we will consider that R is a near-ring and G is an R-group. We initiate the study of monogenic and strongly monogenic R-groups and their basic properties. Also, we investigate some properties of D.G. R-groups, faithful R-groups and monogenic R-groups and we determine that when near-rings are rings.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.57-64
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• 2006

It is proved that if G is a direct sum of countable abelian $p$-groups and R is a special selected commutative unitary highly-generated ring of prime characteristic $p$, which ring is more general than the weakly perfect one, then the group of all normed units V (RG) modulo G, that is V (RG)=G, is a direct sum of countable groups as well. This strengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), that treats the same question but over a perfect ring.

• 대한수학회보
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• 제50권4호
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• 대한수학회지
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• 제52권3호
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• pp.489-501
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• 2015

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

• 대한수학회지
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• 제55권5호
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• pp.1257-1268
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• 2018

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

• 대한수학회보
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• 제45권1호
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• pp.101-103
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• 2008

The structure of $I_G^n/I_G^{n+1}$ for finite abelian group G is investigated.

• 호남수학학술지
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• 제5권1호
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• pp.129-132
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• 1983

• East Asian mathematical journal
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• 제10권1호
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• pp.47-51
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• 1994

• 한국운동역학회지
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• 제21권1호
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• pp.17-24
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• 2011

The Youth Olympic Games(YOG) is an international multi-sport event first held in Singapore from August 14 to August 26, 2010. The idea for such an event was introduced by International Olympic Committee(IOC). The Federation of International Gymnastics(2009) designed the Code of Points and regulates for junior gymnastics at this time. The purpose of this study was to give crucial information and adapt to coaches and junior gymnasts at the time of changing code rapidly. For this study, The eight finalists rings exercise at the 1st Youth Olympic Games was recorded using a digital camcoder. The exercise contents analysis of rings was carried out by an experienced international judge using Code of Points(FIG, 2009). The C elements in various difficulties were performed the highest frequency. The elements group I was the most frequently performed in overall difficulties. Moreover, All the gymnasts performed the elements of the Jonasson and Yamawaki in Group I. Therefore, junior gymnasts need to consider Jonasson and Yamawaki elements correctly in elements group I. The 1st ranked ROU(132) gymnast performed high difficulty value for his routine with the highest E score(9.050). The average of D score were 5.125. In the E scores, 8th USA(140) gymnast received the lowest E score of 8.15, 5th MGL(127) gymnasts received the fewer E score of 8.475. Coaches and junior gymnasts should try to increase D score above 5.125 by higher swing elements in Group I and II as well, decrease deduction of elements in exercise contents.

• 대한수학회논문집
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• 제11권1호
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• pp.63-70
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• 1996

Let K be a field of characteristic 0 and G a Klein's four group. We find the idempotent elements and units of the group ring KG by using the basic group table matrix of G.