• Bulletin of the Korean Chemical Society
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• v.29 no.2
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• pp.377-380
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• 2008

Ground state structures and ring flipping transition states of eight- and seven-membered silicon containing heterocyclic compounds such as dithienodisilacyclooctatriene and oxadithienodisilacycloheptadiene derivatives, respectively have theoretically been investigated. Although the bithienylene moiety of the derivatives does not change the ground state structures, they significantly increase the ring flipping barrier by 13-17 kcal/mol in the case of the eight-membered rings (2, 3, and 4) in comparison with that of silicon containing heterocyclic compound 6, chosen as a model. The same moiety increases the flipping barrier of seven-membered ring (5) is only slightly (3.3 kcal/mol) in comparison with that of model compound 7. Hence, it has been concluded that not only the existing ring strain of eight-membered ring but also the bithienylene moiety collectively increases the ring flipping barrier so as to prevent such conformational changes explaining anomalous NMR behaviour of dithienodisilacyclooctatriene derivatives (2-4). In contrast, the effect of substituents R1 and R2 at the olefinic carbons of the eight-membered ring on the flipping barrier turned out to be mild.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1003-1015
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• 2005

Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.05a
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• pp.145-150
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• 2002

Tubular joints having a large diameter in the offshore structure are reinforced using internal ring stiffener in order to increase the load carrying capacity. In this study, the static strengths of internally ring-stiffened tubular T-joints subjected to compressive brace loading are assessed. Nonlinear finite element analyses are used to compute the behavior of unstiffened and ring-stiffened T-joints. From the numerical results, internal ring stiffener is found to efficient in improving the ultimate capacity, and reinforcement effect are calculated. The influence of geometric parameters for members and ring is evaluated. Based on the FE results, regression analysis is performed considering practical sizes of ring stiffener, finally strength estimation formulae for ring-stiffened T-joints are proposed.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.363-372
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• 2007

An element $a$ in a ring R is called left morphic if $$R/Ra{\simeq_-}1(a)$$. A ring is called left morphic if every element is left morphic. In this paper, an element $a$ in a ring R is called left ${\pi}$-morphic (resp. left G-morphic) if there exists a positive number $n$ such that $a^n$ (resp. $a^n{\neq}0$) is left morphic. A ring R is called left ${\pi}$-morphic (resp. left G-morphic) if every element is left ${\pi}$-morphic (resp. left G-morphic). The Morita invariance of left ${\pi}$-morphic (resp. left G-morphic) rings is discussed. Several relevant properties are proved. In particular, it is shown that a left Noetherian ring R with $M_4(R)$ left G-morphic or $M_2(R)$ left morphic is QF. Some known results of left morphic rings are extended to left G-morphic rings and left ${\pi}$-morphic rings.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.127-132
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• 2007

In this paper, we show that if R is a commutative ring with identity and (S, ${\leq}$) is a strictly totally ordered monoid, then the ring [[$R^{S,{\leq}}$]] of generalized power series is a PF-ring if and only if for any two S-indexed subsets A and B of R such that $B{\subseteq}ann_R(|A)$, there exists $c{\in}ann_R(A)$ such that $bc=b$ for all $b{\in}B$, and that for a Noetherian ring R, $[[R^{S,{\leq}}$]] is a PP ring if and only if R is a PP ring.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.397-406
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• 2013

A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that $l(x)(r(x))$ is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.

• Proceedings of the KIEE Conference
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• 1999.07d
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• pp.1686-1688
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• 1999

The FLR(Field Limiting Ring) structure with a buried ring is proposed to improve breakdown voltage. The breakdown characteristics of proposed structure is verified by two-dimensional device simulator. ATLAS. It has shown that the breakdown voltage of the proposed structure is increased by 11 % compared with that of the FLR.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.195-204
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• 2016

We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].

• Honam Mathematical Journal
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• v.37 no.4
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• pp.377-386
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• 2015

The symmetric ring property was due to Lambek and provided many useful results in relation with noncommutative ring theory. In this note we consider this property over centers, introducing symmetric-over-center. It is shown that symmetric and symmetric-over-center are independent of each other. The structure of symmetric-over-center ring is studied in relation to various radicals of polynomial rings.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.641-649
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• 2007

We in this note introduce a concept, so called ${\pi}-Armendariz$ ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of ${\pi}-Armendariz$ rings, constructing typical examples. We next extend the class of ${\pi}-Armendariz$ rings, through various ring extensions.