• 대한수학회지
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• 제47권5호
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.23-28
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• 2013

The structures of finite local rings of order ${\leq}$ 16 with nonzero Jacobson radical are investigated. The whole shape of non-commutative local rings of minimal order is completely determined up to isomorphism.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1998년도 제27회 춘계학술대회
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• pp.206-211
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• 1998

This paper presents the deformation characteristics of cam ring in a balanced type vane pump. Cam ring is operated in the condition of high pressure. Therefore the local deformation of cam ring affects the characteristics of compression, vane motion and noise and vibration. We analyzed the deformation of cam ring in three types by using the finite element method. As results of analysis, deformed shape of cam ring and the effects of deformation on the compression are presented.

• 호남수학학술지
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• 제23권1호
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• pp.1-4
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• 2001

In [2, 7.3.2], the set of attached prime ideals of local cohomology module $H_m^n(M)$ were calculated, where (A, m) be Noetherian local ring, M finite A-module and $dim_A(M)=n$, and also in the special case in which furthermore A is a homomorphic image of a Gornestien local ring (A', m') (see [2, 11.3.6]). In this paper, we shall obtain this set, by another way in this special case.

• 대한수학회보
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• 제59권2호
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• pp.265-276
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• 2022

In this paper, we introduce duadic codes over finite local rings and concentrate on quadratic residue codes. We study their properties and give the comprehensive method for the computing the unique idempotent generator of quadratic residue codes.

• 대한수학회논문집
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• 제33권4호
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• pp.1049-1053
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• 2018

It is shown that any equidimensional local ring which has finite Cousin cohomology modules with respect to the dimension filtration has a uniform local cohomological annihilator and is universally catenary.

• 대한수학회지
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• 제46권4호
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• pp.675-689
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• 2009

As a sequel to the papers [2, 3], we will complete our identification of the groups of units of the finite local rings $\mathbb{Z}_4$[X]/($X^k$ + 2t(X), $2X^{\gamma}$) which is the most general type of finite local rings with a single nilpotent generator over $\mathbb{Z}_4$.

• 한국소음진동공학회논문집
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• 제18권11호
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• pp.1170-1176
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• 2008

In this study, we propose a new method to control both the beat clarity and beat period in a ring structure. An equivalent ring which satisfies the measured mode condition is determined by using the equivalent ring theory. Theoretical analysis and finite element analysis on the equivalent ring are performed to investigate the effect of the local structural modification on the beat clarity and beat period. Beat clarity and period are improved by attaching asymmetric mass or decreasing local thickness. Through the analysis on the equivalent ring, the proper position and the amount of the local variation are determined to satisfy the required clarity and period condition. All the analysis results are compared and verified by the experiment.

• 한국음향학회지
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• 제27권7호
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• pp.365-371
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• 2008

본 연구에서는 미소 비대칭 링을 대상으로, 맥놀이의 주기를 조절하는 실용적 기법을 제시한다 미세한 비대칭성은 하나의 링 모드를 근접한 주파수를 갖는 모드 쌍으로 분리시키는데, 이 모드 쌍이 동시에 가진되면 근접한 주파수 성분이 간섭함으로써 진동과 음향의 맥놀이가 발생한다. 단순화된 종형상의 링 시편을 대상으로 모드 쌍 데이터를 정밀 측정하고, 측정된 모드 쌍 조건을 만족하는 등가 링 모델을 만든다. 등가 링에 대한 유한요소해석을 통하여, 질량을 부착시키거나 두께를 감소시킬 때, 모드 쌍의 조건 변화를 예측하고 맥놀이 주기를 조절하는 방법을 제시한다. 구조변경에 따른 맥놀이 주기 변화의 예측치와 측정치를 비교하여 제시된 맥놀이 조절기법의 타당성을 검증한다.

• 대한수학회보
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• 제56권3호
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• pp.659-666
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• 2019

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.