• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.83-91
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• 2023

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring M_n(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.213-227
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• 2022

We discuss the relation between units and nilpotents of a ring, concentrating on the transitivity of units on nilpotents under regular group actions. We first prove that for a ring R, if U(R) is right transitive on N(R), then Köthe's conjecture holds for R, where U(R) and N(R) are the group of all units and the set of all nilpotents in R, respectively. A ring is called right UN-transitive if it satisfies this transitivity, as a generalization, a ring is called unilpotent-IFP if aU(R) ⊆ N(R) for all a ∈ N(R). We study the structures of right UN-transitive and unilpotent-IFP rings in relation to radicals, NI rings, unit-IFP rings, matrix rings and polynomial rings.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.215-223
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• 2007

We in this note introduce the concept of NCI rings which is a generalization of NI rings. We study the basic structure of NCI rings, concentrating rings of bounded index of nilpotency and von Neumann regular rings. We also construct suitable examples to the situations raised naturally in the process.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1205-1213
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• 2020

Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce a subclass of the class of 1-absorbing primary ideals called the class of strongly 1-absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ ${\sqrt{0}}$. Firstly, we investigate basic properties of strongly 1-absorbing primary ideals. Hence, we use strongly 1-absorbing primary ideals to characterize rings with exactly one prime ideal (the UN-rings) and local rings with exactly one non maximal prime ideal. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the prime ideals, the primary ideals and the 1-absorbing primary ideals. In the end of this paper, we give an idea about some strongly 1-absorbing primary ideals of the quotient rings, the polynomial rings, and the power series rings.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.87-94
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• 2007

We in this note introduce the concept of g-IFP rings which is a generalization of IFP rings. We show that from any IFP ring there can be constructed a right g-IFP ring but not IFP. We also study the basic properties of right g-IFP rings, constructing suitable examples to the situations raised naturally in the process.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.321-328
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• 2019

We completely characterize the isomorphic class of those associative unitary rings whose elements are sums of four commuting idempotents. Our main theorem enlarges results due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Tang et al. (Lin. & Multilin. Algebra, 2019), Ying et al. (Can. Math. Bull., 2016) as well as results due to the author in (Alban. J. Math., 2018), (Gulf J. Math., 2018), (Bull. Iran. Math. Soc., 2018) and (Boll. Un. Mat. Ital., 2019).

• Honam Mathematical Journal
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• v.29 no.4
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• pp.555-567
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• 2007

We first find strongly 2-primal rings whose sub direct product is not (strongly) 2-primal. Moreover we observe some kinds of ring extensions of (strongly) 2-primal rings. As an example we show that if R is a ring and M is a multiplicative monoid in R consisting of central regular elements, then R is strongly 2-primal if and only if so is $RM^{-1}$. Various properties of (strongly) 2-primal rings are also studied.

• International Journal of Contents
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• v.9 no.3
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• pp.48-54
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• 2013

This paper explores J. R. R. Tolkien's fantasy novel, The Lord of the Rings Trilogy in order to analogize two primary sources which enabled the fantasy literature to be restored to its former popularity in 1930's-50's. First source is the cinematization of the original novel, based on the advanced digital technology, and second, the adaptation of Norse mythology to the original novel. The advanced digital technology rendered a distinguished contribution to the resurrection of the fantasy novel today. Peter Jackson, the director of the film trilogy, The Lord of the Rings Trilogy gained an un-heard popularity in the history of the fantasy movie. It was practicable with the advanced digital technology. Nevertheless, it could be realized only with the fact that J. R. R. Tolkien's original novel retains the excellence of plot. The episodes of the novel present the author's broad knowledge of Norse mythology and his attempts to employ it to the novel, The Lord of the Rings Trilogy. Through such two directions, this paper describes that the advanced digital technology and the quality of the original plot are two key elements to succeed in authoring and filming the fantasy literature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.07a
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• pp.396-399
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• 2003

4H-SiC un diodes with field limiting rings(FLRs) were fabricated and characterized. The dependences of reverse breakdown voltage on the number of FLRs, the distance between p-base main junction and first FLR, and activation temperatures, were investigated. Al and B ions were implanted and activated at high temperature to form p-base region and p+ region in the n-epilayer. We have obtained up to 1782V of reverse breakdown voltage in the un diode with two FLRs on loom thick epilayer. The differential on-resistances of the fabricated diode are $5.3m{\Omega}cm^2$ at $100A/cm^2$ and $2.7m{\Omega}cm^2$ at $1kA/cm^2$, respectively. All pn diodes with FLRs have higher avalanche breakdown voltages than that of diode without an FLR. Regardless of the activation temperature, the un diode with a FLR located 5um apart from main junction has the highest mean breakdown voltage around 1600V among the diodes with one ring. On the other hand, the pn diode with two rings showed different behavior with activation temperature. It reveals that high voltage SiC pn diodes with low on-resistance can be fabricated by using the FLR edge termination.

• Korean Journal of Materials Research
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• v.23 no.8
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• pp.453-461
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• 2013

Controlling the stick and slip motions of the contact lines in a confined geometry comprised of a spherical lens with a flat substrate is useful for manufacturing polymer ring patterns. We used a sphere on a flat geometry, by which we could control the interfaces of the solution, vapor and substrate. By this method, hundreds of concentric ring-pattern formations of a linear conjugated polymer, poly [2-methoxy-5-(2-thylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV), were generated with excellent regularity over large areas after complete solvent evaporation. Subsequently, the MEH-PPV ring patterns played a role as a directed template to organize highly regular concentric rings of single-walled carbon nanotubes(SWCNTs); when a droplet of the SWCNT suspension in water was casted onto the prepared substrate, hydrophobic polymer patterns confined the water dispersed SWCNTs in between the hydrophilicized $SiO_2/Si$ substrate. As the solvent evaporated, SWCNT-rings were formed in between MEH-PPV rings with controlled density. Finally, we used a lift-off process to produce SWCNT patterns by the removal of a sacrificial polymer template with organic solvent. We also fabricated a field effect transistor using self-assembled SWCNT networks on a $SiO_2/Si$ substrate.