• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.123-129
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• 2014

In this paper the concepts of pure ideals, weakly pure ideals and purely prime ideals in ordered semigroups are introduced. We obtain some characterizations of pure ideals and prove that the set of all pure prime ideals is topologized.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.455-465
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• 2020

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.33-40
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• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

• Analytical Science and Technology
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• v.23 no.3
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• pp.233-239
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• 2010

Pure macroporous silica matrix using a template of polystyrene (PS) was prepared by the sol-gel method. Macroporous Ag-$SiO_2$ composite materials, which were homogeneously dispersed with Ag particles in the macropores, were successfully fabricated. The pure porous silica had ordered pore sizes of 100 nm and 200 nm, which was adjusted under consideration of the template size. The macroporous Ag-$SiO_2$ composite showed the ideal ordered distribution of the pore in case of the adding of 3 wt% $AgNO_3$ under consideration of controlling of the pore size as well as microstructural observation of $AgNO_3$concentration. The macroporous Ag-$SiO_2$ composites had ordered 100 nm and 200 nm pores, and the Ag particles within the matrix showed the size of 15~20 nm.