• Communications of the Korean Mathematical Society
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• v.33 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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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 $x,y{\in}X(R)$.

• Journal of the Korean Chemical Society
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• v.9 no.3
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• pp.134-141
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• 1965

Crystals of nicotine dihydroiodide, are orthorhombic with space group $p2_12_12_1$.The unit cell of dimensions a=7.61, b=11.01, e=17.27${\AA}$, contains four formula units. The structure has been determined by X-ray diffraction method and has been refined to give the R-index, ${\sum}{\mid}{\mid}F_{\circ}{\mid}-{\mid}F_c{\mid}{\mid}{\div}{\sum}{\mid}F_{\circ}{\mid}$, of 0.16 and 0.14 for $F_{okl}\;and\;F_{hol}$ respectively.The mean lengths of C-C and C-N bonds in pyridine ring are 1.40 and $1.35{\AA}$ and those in pyrolidine ring 1.56 and $1.48{\AA}$ respectively, though accurate measurement of bond length has not been attempted. The six atoms in the pyridine ring are coplanar and on the other hand $C_6,\;C_7,\;C_8$ and $N_2$ atoms in pyrrolidine ring form a plane within accuracy of the analysis, and $C_9$ atom is distant $0.22{\AA}$ out of the plane consist of $C_6,\;C_7,\;C_8$ and $N_2$ aoms. The normals to the two planes form an angle of $94^{\circ}$ with each other. Iodine atom is distant $3.55{\AA}$ from nitrogen atom in pyridine ring and the other iodine atom $3.58{\AA}$ from nitrogen atom in pyrrolidine ring, so that the nitrogen and iodine atoms are firmly linked.It seems that the only forces binding nicotine dihydroiodide molecules together in the crystal are Van der Waals forces.

• Honam Mathematical Journal
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• v.21 no.1
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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 $r(1)=0,\;\frac{1}{{\mid}G{\mid}},\;\frac{2}{{\mid}G{\mid}},\;{\cdots},\frac{{\mid}G{\mid}-1}{{\mid}G{\mid}},\;1$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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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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• v.25 no.2
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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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• v.7 no.4
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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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.10a
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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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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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.