• 한국수학교육학회지시리즈E:수학교육논문집
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• 제10권
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• pp.283-292
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• 2000

We shall introduce new concepts of near-rings, that is, strong reducibility and left semi ${\pi}$-regular near-rings. We will study every strong reducibility of near-ring implies reducibility of near-ring but this converse is not true, and also some characterizations of strong reducibility of near-rings. We shall investigate some relations between strongly reduced near-rings and left strongly regular near-rings, and apply strong reducibility of near-rings to the study of left semi ${\pi}$-regular near-rings, s-weekly regular near-rings and some other regularity of near-rings.

• East Asian mathematical journal
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• 제22권1호
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• pp.61-69
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• 2006

A near-ring N is reduced if, for $a{\in}N,\;a^2=0$ implies a=0, and N is left strongly regular if for all $a{\in}N$ there exists $x{\in}N$ such that $a=xa^2$. Mason introduced this notion and characterized left strongly regular zero-symmetric unital near-rings. Several authors ([2], [5], [7]) studied these properties in near-rings. Reddy and Murty extended some results in Mason to the non-zero symmetric case. In this paper, we will define a concept of strong reducedness and investigate a relation between strongly reduced near-rings and left strongly regular near-rings.

• 대한수학회보
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• 제44권3호
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• pp.407-414
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• 2007

In [12], McCoy proved that if R is a commutative ring, then whenever g(x) is a zero-divisor in R[x], there exists a nonzero c $\in$ R such that cg(x) = 0. In this paper, first we extend this result to monoid rings. Then for a monoid M, we give some examples of M-quasi-Armendariz rings which are a generalization of quasi-Armendariz rings. Every reduced ring is M-quasi-Armendariz for any unique product monoid M and any strictly totally ordered monoid $(M,\;{\leq})$. Also $T_4(R)$ is M-quasi-Armendariz when R is reduced and M-Armendariz.

• 대한수학회지
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• 제53권2호
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• pp.403-414
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• 2016

Let R be a ring, and let M be a left R-module. If M is Rad-supplementing, then every direct summand of M is Rad-supplementing, but not each factor module of M. Any finite direct sum of Rad-supplementing modules is Rad-supplementing. Every module with composition series is (Rad-)supplementing. M has a Rad-supplement in its injective envelope if and only if M has a Rad-supplement in every essential extension. R is left perfect if and only if R is semilocal, reduced and the free left R-module $(_RR)^{({\mathbb{N})}$ is Rad-supplementing if and only if R is reduced and the free left R-module $(_RR)^{({\mathbb{N})}$ is ample Rad-supplementing. M is ample Rad-supplementing if and only if every submodule of M is Rad-supplementing. Every left R-module is (ample) Rad-supplementing if and only if R/P(R) is left perfect, where P(R) is the sum of all left ideals I of R such that Rad I = I.

• 대한수학회보
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• 제48권1호
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• pp.157-167
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• 2011

For a ring endomorphism of a ring R, Krempa called $\alpha$ rigid endomorphism if $a{\alpha}(a)$ = 0 implies a = 0 for a $\in$ R, and Hong et al. called R an $\alpha$-rigid ring if there exists a rigid endomorphism $\alpha$. Due to Rege and Chhawchharia, a ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. The Armendariz property of polynomials was extended to one of skew polynomials (i.e., $\alpha$-Armendariz rings and $\alpha$-skew Armendariz rings) by Hong et al. In this paper, we study the relationship between $\alpha$-rigid rings and extended Armendariz rings, and so we get various conditions on the rings which are equivalent to the condition of being an $\alpha$-rigid ring. Several known results relating to extended Armendariz rings can be obtained as corollaries of our results.

• 대한전자공학회논문지TC
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• 제44권12호
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• pp.22-27
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• 2007

본 논문에서는 마이크로스트립 사각 개방 루프 Split Ring 공진기 (OLSRR)를 이용하여 개선된 전압 제어 발진기를 위상 잡음을 줄이기 위하여 제안하였다. 이 목적을 위하여 마이크로스트립 사각 개방 루프의 형태를 갖는 사각형의 Split Ring 공진기에 대하여 연구하였다. 마이로스트립 사각 개방 루프 공진기와 비교할 경우, 마이크로스트립 사각 개방 루프 Split Ring 공진기는 더 큰 결합 계수를 갖으며, 이로 인하여 얻을 수 있는 더 높은 Q 값을 통하여 전압 제어 발진기의 위상 잡음을 줄일 수 있다. 1.7 V의 공급 전력을 갖는 전압 제어 발진기는 주파수 조절 범위, $5.746\sim5.854$ GHz에서 $-120\sim-116.5$ dBc/Hz @ 100 kHz의 위상 잡음 특성을 갖는다. 이 전압 제어 발진기의 FOM은 같은 주파수 조절 범위에서 $-200.33\sim-197$ dBc/Hz @ 100 kHz를 갖는다.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.437-453
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• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• Bulletin of the Korean Chemical Society
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• 제15권2호
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• pp.132-138
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• 1994

Bis(diethylamino)aluminum hydride was utilized in a systematic study of the approximate rates and stoichiometry of the reaction of excess reagent with 55 selected organic compounds containing representative functional groups under standardized conditions (THF, $0^{\circ}C$, reagent to compound=4 : 1) in order to define the characteristics of the reagent for selective reductions. The reducing action of BEAH was also compared with that of the parent aluminum hydride. The reducing action of the reagent is quite similar to that of aluminum hydride, but the reducing power is much weaker. Aldehydes and ketones were readily reduced in 1-3 h to the corresponding alcohols. However, unexpectedly, a ready involvement of the double bond in cinnamaldehyde was realized to afford hydrocinnamyl alcohol. The introduction of diethylamino group to the parent aluminum hydride appears not to be appreciably influential in stereoselectivity on the reduction of cyclic ketones. Both p-benzoquinone and anthraquinone utilized 2 equiv of hydride readily without evolution of hydrogen, proceeded cleanly to the 1,4-reduction products. Carboxylic acids and acid chlorides underwent reduction to alcohols slowly, whereas cyclic anhydrides utilized only 2 equiv of hydride slowly to the corresponding hydroxylacids. Especially, benzoic acid with a limiting amount of hydride was reduced to benzaldehyde in a yield of 80%. Esters and lactones were also readily reduced to alcohols. Epoxides examined all reacted slowly to give the ring-opened products. Primary and tertiary amides utilized 1 equiv of hydride fast and further hydride utilization was quite slow. The examination for possibility of achieving a partial reduction to aldehydes was also performed. Among them, benzamide and N,N-dimethylbenzamide gave ca, 90% yields of benzaldehyde. Both the nitriles examined were also slowly reduced to the amines. Unexpectedly, both aliphatic and aromatic nitro compounds proved to be relatively reactive to the reagent. On the other hand, azo- and azoxybenzenes were quite inert to BEAH. Cyclohexanone oxime liberated 1 equiv of hydrogen and utilized 1 equiv of hydride for reduction, corresponding to N-hydroxycyclohexylamine. Pyridine ring compounds were also slowly attacked. Disulfides were readily reduced with hydrogen evolution to the thiols, and dimethyl sulfoxide and diphenyl sulfone were also rapidly reduced to the sulfides.

• Archives of Pharmacal Research
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• 제23권1호
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• pp.35-41
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• 2000

In order to investigate the stereochemical requirements of planar structure at 4-position of 4-phenyl-1-arylsulfonylimidazolidinones (1) for their cytoxicities against human cancer cell lines, the size, the distance from imidazolidinone ring, and the conformation of this moiety were variegated. Replacement of phenyl moiety with naphthyl in compounds 2 and 3 or benzyl moiety in compound 4 sharply reduced activity of 1. Conformational restriction on phenyl ring in compound 5 also resulted in the loss of activity of 1. Therefore, phenyl moiety without any substituents directly attached to imidazolidinone ring of 1 should be considered as an essential pharmacophore for this analog.

• 산업기술연구
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• 제22권A호
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• pp.29-36
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• 2002

A damage detection algorithm using vibration modes is applied to the ring structures and the modal behaviors of the slightly asymmetric rings are examined. Mode shape change, MSER(modal strain energy ratio) and MCR(modal curvature ratio) are investigated to identify the locations of faults or damages The above fault detection parameters are calculated and compared by the finite element analysis on rings with designed local damages. Damages are modeled as a reduced stiffness in the analysis The results show that MSER and MCR can be proper parameters to detect local damages in the ring structures.