• Communications of Mathematical Education
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• v.10
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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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• v.22 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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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.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.12
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• pp.22-27
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• 2007

In this paper, a novel voltage-controlled oscillator (VCO) using the microstrip square open loop split ring resonator (OLSRR) is presented for reducing the phase noise. For this purpose, the square-shaped split ring resonator (SRR) haying the form of the microstrip square open loop is investigated. Compared with the microstrip square open loop resonator, the microstrip square OLSRR has the larger coupling coefficient value, which makes a higher Q value, and has reduced the phase noise of VCO. The VCO with 1.7V power supply has the phase noise of $-120\sim-116.5$ dBc/Hz @ 100 kHz in the tuning range, $5.746\sim5.854$ GHz. The figure of merit (FOM) of this VCO is $-200.33\sim-197$ dBc/Hz @ 100 kHz in the same tuning range.

• Kyungpook Mathematical Journal
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• v.62 no.3
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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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• v.15 no.2
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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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• v.23 no.1
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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.

• Journal of Industrial Technology
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• v.22 no.A
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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.