• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1367-1383
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• 2021

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into a numerical semigroup and its dual. It is also given exactly for what kind of numerical semigroup S, the semigroup ring 𝕜⟦S⟧ has at least one Gorenstein subring and has at least one Kunz subring.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.343-347
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• 2010

In this paper we study the connection between 2-primal rings, (S,1)-rings and related conditions. And we investigate some condition which is the special case of pseudo symmetric. We also study the condition (KJ) which is given by J. Y. Kim and H. L. Jin. We introduce some condition and we prove that our condition is equivalent to the condition (KJ) when it is an (S,1)-ring.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-156
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• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• Korean Journal of Crystallography
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• v.10 no.1
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• pp.1-8
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• 1999

Two conformational isomers of p-tert-butylcalix[4]arene hexanoate were prepared from the reaction of-p-tert-butylcalix[4]arene and hexanoly chloride in the presence of AlCl3 in CH2Cl2 and their structures were determined by NMR spectra and X-ray diffraction as a cone and a 1,3-alternate conformer, respectively. The crystal of cone conformer (C68H96O8·(CH3)2CO) is triclinic, P, a=15.066(1) , b=16.063(1) , c=16.365(1) , α=79.75(2)o, β=109.95(2)o, γ=80.32(0)o, V=3602.7(4) 3, Z=2. The intensity data were collected on Simens SMART diffractometer/CCD area detector. The structure was solved by direct method and refined by least-squares calculations to a final R value of 0.144 for 4638 observed reflections. The molecular conformation is distorted symmetric cone with the flattening A and D phenyl rings. The crystal of 1,3-alternate conformer (C68H96O8·2CHCl3) is orthorhombic, Pca21, a=34.586(5) , b=10.207(3) , c=20.394(4) , V=7199(3) 3, Z=4. The intensity data were collected on an Enraf-Noninus CAD-4 Diffractometer with a graphite monochromated Mo-K radiation. The structure was solved by direct method and refined by least-squares calculations to a final R value of 0.152 for 2241 observed reflections. The molecule has a pseudo mirror symmetric 1,3-alternate conformation.