• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.21-30
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• 2007

We say a module $M_R$ a semicommutative module if for any $m{\in}M$ and any $a{\in}R$, $ma=0$ implies $mRa=0$. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p.p. and p.q.-Baer rings to extend to modules. In addition we also prove, for a p.p.-ring R, R is semicommutative iff R is Armendariz. Let R be an abelian ring and $M_R$ be a p.p.-module, then $M_R$ is a semicommutative module iff $M_R$ is an Armendariz module. For any ring R, R is semicommutative iff A(R, ${\alpha}$) is semicommutative. Let R be a reduced ring, it is shown that for number $n{\geq}4$ and $k=[n=2]$, $T^k_n(R)$ is semicommutative ring but $T^{k-1}_n(R)$ is not.

• 대한수학회논문집
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• 제39권2호
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• pp.267-278
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• 2024

In this paper, we continue to explore an idea presented in [3] and introduce a new class of matrix rings called staircase matrix rings which has applications in noncommutative ring theory. We show that these rings preserve the notions of reduced, symmetric, reversible, IFP, reflexive, abelian rings, etc.

• 대한수학회논문집
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• 제25권3호
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• pp.349-364
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• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, $b\;{\in}\;R$. Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and $\alpha$ an endomorphism of R, we say that R is right (resp., left) $\alpha$-shifting if whenever $a{\alpha}(b)\;=\;0$ (resp., $\alpha{a)b\;=\;0$) for a, $b\;{\in}\;R$, $b{\alpha}{a)\;=\;0$ (resp., $\alpha(b)a\;=\;0$); and the ring R is called $\alpha$-shifting if it is both left and right $\alpha$-shifting. We investigate characterizations of $\alpha$-shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism $\alpha$ of a ring R, R is right (resp., left) $\alpha$-shifting if and only if Q(R) is right (resp., left) $\bar{\alpha}$-shifting, whenever there exists the classical right quotient ring Q(R) of R.

• East Asian mathematical journal
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• 제33권1호
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• pp.75-81
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• 2017

It is a well-known fact that a ring R is regular if and only if every left R-modules is flat. In this article we prove that a ring R is strongly regular if and only if every left R-modules is reduced if and only if every left-R modules is quasi-reduced.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.29-34
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• 2013

Power-Armendariz is a unifying concept of Armendariz and commutative. Let R be a ring and I be a proper ideal of R such that R/I is a power-Armendariz ring. Han et al. proved that if I is a reduced ring without identity then R is power-Armendariz. We find another direct proof of this result to see the concrete forms of various kinds of subsets appearing in the process.

• 대한수학회논문집
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• 제34권3호
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• pp.719-727
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• 2019

This article concerns a generalization of Armendariz rings that is done by restricting the degree to one. We shall call such rings, as to satisfy this property, partial-Armendariz. We first show that partial-Armendariz rings are between Armendariz rings and weak Armendariz rings. The basic structures of partial-Armendariz rings are investigated, and the relations between partial-Armendariz rings and near related ring properties are also studied.

• 대한수학회보
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• 제59권5호
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• pp.1237-1246
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• 2022

In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it a mid ring. Also, we provide new characterizations for von Neumann regular and zero-dimensional rings. Moreover, some results about mp-ring are given. Finally, a characterization for mid rings is provided. Then it is shown that the class of mid rings is strictly between the class of reduced mp-rings (p.f. rings) and the class of mp-rings.

• 대한수학회논문집
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• 제33권4호
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• pp.1083-1096
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• 2018

Let R be an associative ring. We define a subset $S_R$ of R as $S_R=\{a{\in}R{\mid}aRa=(0)\}$ and call it the source of semiprimeness of R. We first examine some basic properties of the subset $S_R$ in any ring R, and then define the notions such as R being a ${\mid}S_R{\mid}$-reduced ring, a ${\mid}S_R{\mid}$-domain and a ${\mid}S_R{\mid}$-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite ${\mid}S_R{\mid}$-domain is necessarily unitary, and is in fact a ${\mid}S_R{\mid}$-division ring. However, we provide an example showing that a finite ${\mid}S_R{\mid}$-division ring does not need to be commutative. All possible values for characteristics of unitary ${\mid}S_R{\mid}$-reduced rings and ${\mid}S_R{\mid}$-domains are also determined.

• Tribology and Lubricants
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• 제25권5호
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• pp.348-358
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• 2009

To satisfy the more severe emission regulation and the demand of higher fuel economy in near future, the combustion pressure and power output of engines is going to be higher. In order to get the reduction of engine emission and the higher power, it is needed the reduction of the tension and width of ring pack. The lower tension ring and the manufacturing technology of cast iron thinner width ring can bring the friction reduction between the ring and liner during engine running. Therfore, the fuel economy can be achieved. Thereafter the engine emission can be reduced. In this study, by using a developed basic computer program that predicts the inter-ring pressure, the motion of ring and the inter-ring pressure through a crevice volume model between adjacent rings, and the oil film thickness and the friction computed by lubrication theories, it is to be examined the effect of friction reduction from piston ring pack equipped with thinner width ring and lower tension ring.

• 한국산학기술학회논문지
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• 제15권5호
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• pp.3139-3145
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• 2014

본 논문에서는 가유전체 기판을 이용하여 소형화한 마이크로파 대역의 링 하이브리드 커플러 설계에 대하여 기술한다. 가유전체 기판은 다수의 비어홀을 제 2기판에 삽입하여 유효 커패시턴스를 크게 증가시킨 구조를 갖는다. 가유전체 기판의 유효유전율은 표준형 기판에 비하여 크게 증가하게 되는데, 이에 의하여 동일한 전기적 길이 대비 물리적 길이가 크게 감소하므로 마이크로파 전송선로를 소형화시킬 수 있다. 이런 원리를 마이크로파 무선회로 설계에 적용한 사례를 보이기 위하여 가유전체 기판을 이용하여 3GHz대 링 하이브리드 커플러를 설계하고 실제로 제작 및 측정한 결과를 제시한다. 설계된 소형화된 링 하이브리드 커플러는 표준형에 비하여 전기적 성능은 유사하면서도 65%의 크기를 가진다. 측정된 전력분배비는 각각 -3.05dB와 -3.135dB이며, 두 출력간의 위상차는 동위상일 때 3도, 역위상일 때 176도로 이상적인 값과 매우 유사하다. 이로써 가유전체 기판구조로 소형화된 링 하이브리드 커플러의 설계가 타당함을 보인다.