• 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.

• 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.

• 대한수학회지
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• 제51권4호
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• pp.655-663
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• 2014

Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.

• 대한화학회지
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• 제9권3호
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• pp.134-141
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• 1965

니코틴 二沃化水素酸鹽의 結晶은 直角非等軸結晶係(料方晶係)에 屬하며 空間群은 $p2_12_12_1$이다. 單位格子의 크기는 a=7.61, b=11.01 및 e=17.27${\AA}$이며 單位格子안에 들어있는 化學單位의 水는 4이다. 이 結晶의 構造를 X-線廻折法에 依하여 解析하였으며 R 値 ${\sum}{\mid}{\mid}F_{\circ}{\mid}-{\mid}F_c{\mid}{\mid}{\div}{\sum}{\mid}F_{\circ}{\mid}$ 가 $F_{orl}$와 $_{kol}$에 關하여 各各 0.16및 0.14의 값을 이룰 때까지 精密化 하였다. 原子間距離의 精密化를 試圖하지는 않았지만 피리딘 고리 안의 C-C 및 C-N의平均距離는 各各 1.40 및 $1.35{\AA}$의 값을 가진다. 피리딘 고리 內의 各原子는 實驗誤差內에서 同一平面上에 있으며 피롤리딘 고리에서는 $C_6,\;C_7,\;C_8$및$N_2$原子는 大略 同一平面上에 있으나 $C_9$는 이 平面으로 부터 約0.22${\AA}$ 떨어져있다. 피리딘 고리의 平面과 $C_6,\;C_7,\;C_8$및 $N_2$가 이루는 平面의 各法線은 約 $94^{\circ}$를 이루고 있다. 이코틴 二沃化水素酸鹽의 한 分子內의 두個의 요오드 原子中 한개는 피리딘 고리의 窒素原子와 $3.55{\AA}$의 距離로 連結되여 있으며 다른 한개는 피콜리딘 고리의 窒素原子 와 $3.58{\AA}$의 距離로 連結되여 있다. 結晶內에서 各 分子는 Van der Waals force로 서로 接燭되여 있다.

• 호남수학학술지
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• 제21권1호
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• pp.57-64
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• 1999

Let K be a algebraically closed field of characteristic 0 and G be abelian group $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_4$. We find the conditions which the elements of the group ring KG are unit and idempotent respecting using the basic table matrix of G. We can see that if ${\alpha}={\sum}r(g)g$ is an idempotent element of KG, then $r(1)=0,\;\frac{1}{{\mid}G{\mid}},\;\frac{2}{{\mid}G{\mid}},\;{\cdots},\frac{{\mid}G{\mid}-1}{{\mid}G{\mid}},\;1$.

• 대한수학회보
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• 제53권6호
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• pp.1629-1643
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• 2016

Let R be a ring with identity, X be the set of all nonzero, nonunits of R and G be the group of all units of R. A ring R is called unit-duo ring if $[x]_{\ell}=[x]_r$ for all $x{\in}X$ where $[x]_{\ell}=\{ux{\mid}u{\in}G\}$ (resp. $[x]_r=\{xu{\mid}u{\in}G\}$) which are equivalence classes on X. It is shown that for a semisimple unit-duo ring R (for example, a strongly regular ring), there exist a finite number of equivalence classes on X if and only if R is artinian. By considering the zero divisor graph (denoted ${\tilde{\Gamma}}(R)$) determined by equivalence classes of zero divisors of a unit-duo ring R, it is shown that for a unit-duo ring R such that ${\tilde{\Gamma}}(R)$ is a finite graph, R is local if and only if diam(${\tilde{\Gamma}}(R)$) = 2.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.215-227
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• 2017

Let D be an integral domain with quotient field K, X be an indeterminate over D, K[X] be the polynomial ring over K, and $R=\{f{\in}K[X]{\mid}f(0){\in}D\}$; so R is a subring of K[X] containing D[X]. For $f=a_0+a_1X+{\cdots}+a_nX^n{\in}R$, let C(f) be the ideal of R generated by $a_0$, $a_1X$, ${\ldots}$, $a_nX^n$ and $N(H)=\{g{\in}R{\mid}C(g)_{\upsilon}=R\}$. In this paper, we study two rings $R_{N(H)}$ and $Kr(R,{\upsilon})=\{{\frac{f}{g}}{\mid}f,g{\in}R,\;g{\neq}0,{\text{ and }}C(f){\subseteq}C(g)_{\upsilon}\}$. We then use these two rings to give some examples which show that the results of [4] are the best generalizations of Nagata rings and Kronecker function rings to graded integral domains.

• Current Optics and Photonics
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• 제7권4호
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• pp.457-462
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• 2023

Quantitative measurement of trace ethane is important in environmental science and biomedical applications. For these applications, we typically require a few tens of part-per-trillion level measurement sensitivity. To measure trace-level ethane, we constructed a cavity ring-down spectroscopy setup in the 3.37 ㎛ mid-infrared wavelength range, which is applicable to multi-species chemical analysis. We demonstrated that the detection limit of ethane is approximately 300 parts per trillion, and the measured concentration is in agreement with the amounts of the injected sample. We expect that these results can be applied to the chemical analysis of ethane and applications such as breath test equipment.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2009년도 추계학술대회 논문집
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• pp.72-75
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• 2009

Design and Manufacturing processes of Ti-6Al-4V profiled ring-products were investigated with three-dimensional FEM simulation and experimental analyses. FEM simulation for the ring-rolling process was used to calculate the state variables such as strain, strain rate and temperature. In the simulation results of strain and temperature distributions for a plane ring rolling process, the strain level at the surface area is higher than that at the mid-plane, but the temperature level at the surface area is lower than that at mid-plane due to heat transfer between the workpiece and the work roll. These distributions showed a great influence on the evolution of microstructure in different positions. In order to induce the uniform deformation of the profile ring and reduce the applied load, the final blank was prepared by two-step processes. The mechanical properties of Ti-6Al-4V alloy ring products made in this work were investigated with tensile and impact tests and analyzed with the evolution of microstructures during the ring rolling process.

• 대한수학회보
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• 제39권3호
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• pp.411-422
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• 2002

In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for $0{\neq}e^2=e{\in}R$ if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[$\chi$] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the $K\ddot{o}the's$ conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with $\mid$X$\mid$ $\geq$ 2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.