• 대한수학회보
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• 제35권3호
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• pp.527-532
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• 1998

We study some properties of Schur functor and its sub-functions related to separable algebras and cyclotomic algebras.

• 대한수학회보
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• 제51권6호
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• pp.1689-1696
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• 2014

Recently, it was proved that every p-Schur ring over an abelian group of order $p^3$ is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order $p^3$ is Schurian.

• 대한수학회논문집
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• 제35권4호
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• pp.1087-1093
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• 2020

The aim of this paper is to show that every Engel quasinormal subgroups of the unit group of a division ring with uncountable center is central.

• 대한수학회보
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• 제48권5호
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• pp.1033-1039
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• 2011

Let R be a ring with identity 1, I(R) be the set of all idempotents in R and G be the group of all units of R. In this paper, we show that for any semiperfect ring R in which 2 = 1+1 is a unit, I(R) is closed under multiplication if and only if R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication and eGe is contained in the group of units of eRe. In particular, for a left Artinian ring in which 2 is a unit, R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication.

• Bulletin of the Korean Chemical Society
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• 제6권4호
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• pp.222-224
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• 1985

The crystal structure of sulindac, $C_{20}H_{17}Fo_3S$, one of the nonsteroid antiinflammatory agents, has been determined by the X-ray diffraction techniques using diffractometer data obtained by the $\varpi-2{\theta}$ scan technique with Cu $$K_{\alpha}$$ radiation from a crystal with space group symmetry Pbca and unit cell parameters a = 8.166(1), b = 18.291(8), c = 23.245(10) ${\AA}.$ The structure was solved by direct methods and refined by full-matrix least-squares to a final R = 0.11 for the 1153 observed reflections. The carboxyl group is nearly perpendicular to the indenyl ring as observed in indomethacin. The dihedral angle between the indenyl and phenyl rings is $35^{\circ}while$ the corresponding angle in indomethacin is $67^{\circ}.$ Crystal packing consists of a hydrogen bond and partial ring stacking between the indenyl rings.

• Bulletin of the Korean Chemical Society
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• 제11권4호
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• pp.333-339
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• 1990

A series of new dimesogenic compounds whose mesogens are of aromatic ester or amide type having a trifluoromethyl $(CF_3)$ substituent at the para-position of each terminal phenolic rings were prepared and their liquid crystalline properties were studied by differential scanning calorimetry (DSC) and on a cross-polarizing microscope. The compounds have two identical mesogenic units bracketing a central decamethylene spacer. Trifluoromethyl group appears to favor the formation of smectic phases when it is attached to a phenoxy or anilide terminal. Its group efficiency for mesophase formation seems to be inferior to other common substituents. A thermodynamic analysis of the phase transitions was made and the results were explained in relation to the structures of the compounds.

• East Asian mathematical journal
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• 제22권2호
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• pp.239-248
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• 2006

Let G be a group acting on a ring R. We will define the group action of G on an intuitionsitic fuzzy set of R. We will introduce intuitionistic fuzzy G-prime ideals of a ring and we will prove that every intuitionistic fuzzy G-prime ideal is the largest G-invariant intuitionistic fuzzy ideal of R contained in the intuitionistic fuzzy prime ideal which is uniquely determined up to G-orbits.

• 호남수학학술지
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• 제45권4호
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• pp.678-681
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• 2023

Let G be a cyclic group of prime power order p^k, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/p^kℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in Iⁿ if and only if the i-th derivative of the image of α in ℤ/p^kℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

• Bulletin of the Korean Chemical Society
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• 제18권1호
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• pp.14-18
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• 1997

Sulconazole nitrate, C18H16Cl3N3O3S, crystallizes in monoclinic, space group C2/c, with a=14.401(1), b=8.051(1), c=34.861(2) Å, β=95.9(1)°, g=0.58 mm-1, Dc=1.523 g/cm3, Dm=1.522 g/cm3, F(000)=1888.0, and z=8. Intensities for 2460 unique reflections were measured on a CAD4 diffractometer with graphited-monochromated Mo-Kα radiation. The structure was solved by direct method and refined by full matrix least squares to a final R=0.071 for 2182 reflections (Io > 2σIo). The bond lengths and angles are comparable with the values found in the analogues imidazole derivatives. The 2,4-dichlorophenyl ring(A) and the p-chlorophenyl ring(B) are almost planar with different heights [dihedral angle 17.3°] while the imidazole ring(C) is nearly perpendicular to the two phenyl rings[dihedral angles about the two rings A, B are 110.8° and 96.1° respectively]. In order to understand the overall conformation we calculated the selected distances (l1, l2, l3) among the center of the three rings and considered the imaginary plan D[C(7), C(9) and C(16)]. The two polar group S(8) and N(19) do not have gauche conformation and l2 value (4.47 Å) is shorter than the other imidazole derivatives. One -NO3 group are hydrogen bonded the two neighbored sulconazole molecules. The molecular crystal packing is also formed by two hydrogen bondings and van der Waals forces.

• 대한수학회보
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• 제22권2호
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.