• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.657-664
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• 2004

We investigate skew power series of $\alpha$-rigid p.p.-rings, where $\alpha$ is an endomorphism of a ring R which is not assumed to be surjective. For an $\alpha$-rigid ring R, R[[${\chi};{\alpha}$]] is right p.p., if and only if R[[${\chi},{\chi}^{-1};{\alpha}$]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1957-1972
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• 2013

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization. It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.683-694
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• 2023

Let a be an ideal of 𝔞 commutative noetherian ring R. We give some descriptions of the 𝔞-depth of 𝔞-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaulayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.137-143
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• 1992

The purpose of this paper is to provide the affirmative solution of the following conjecture due to Davis and Geramita. Conjecture; Let A=R[T] be a polynomial ring in one variable, where R is a regular local ring of dimension d. Then maximal ideals in A are complete intersection. Geramita has proved that the conjecture is true when R is a regular local ring of dimension 2. Whatwadekar has rpoved that conjecture is true when R is a formal power series ring over a field and also when R is a localization of an affine algebra over an infinite perfect field. Nashier also proved that conjecture is true when R is a local ring of D[ $X_{1}$,.., $X_{d-1}$] at the maximal ideal (.pi., $X_{1}$,.., $X_{d-1}$) where (D,(.pi.)) is a discrete valuation ring with infinite residue field. The methods to establish our results are following from Nashier's method. We divide this paper into three sections. In section 1 we state Theorems without proofs which are used in section 2 and 3. In section 2 we prove some lemmas and propositions which are used in proving our results. In section 3 we prove our main theorem.eorem.rem.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.37 no.2
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• pp.208-214
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• 2024

This reports the electrical properties of single-crystal β-gallium oxide (β-Ga₂O₃) vertical Schottky barrier diodes (SBDs) with a different guard ring structure. The vertical Schottky barrier diodes (V-SBDs) were fabricated with two types guard ring structures, one is with metal deposited on the Al₂O₃ passivation layer (film guard ring: FGR) and the other is with vias formed in the Al₂O₃ passivation layer to allow the metal to contact the Ga₂O₃ surface (metal guard ring: MGR). The forward current values of FGR and MGR V-SBD are 955 mA and 666 mA at 9 V, respectively, and the specific on-resistance (R_on,sp) is 5.9 mΩ·cm² and 29 mΩ·cm². The series resistance (R_s) in the nonlinear section extracted using Cheung's formula was 6 Ω, 4.8 Ω for FGR V-SBD, 10.7 Ω, 6.7 Ω for MGR V-SBD, respectively, and the breakdown voltage was 528 V for FGR V-SBD and 358 V for MGR V-SBD. Degradation of electrical characteristics of the MGR V-SBD can be attributed to the increased reverse leakage current caused by the guard ring structure, and it is expected that the electrical performance can be improved by preventing premature leakage current when an appropriate reverse voltage is applied to the guard ring area. On the other hand, FGR V-SBD shows overall better electrical properties than MGR V-SBD because Al₂O₃ was widely deposited on the Ga₂O₃ surface, which prevent leakage current on the Ga₂O₃ surface.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.747-755
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• 2013

This paper deals with the unit groups of the endomorphism rings of projective modules over polynomial rings and further over formal power series rings. A normal subgroup of the unit group is defined and discussed. The local splitting properties of element of endomorphism rings of projective modules over polynomial rings are given.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.879-897
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• 2010

Y. Hirano introduced the concept of a quasi-Armendariz ring which extends both Armendariz rings and semiprime rings. A ring R is called quasi-Armendariz if $a_iRb_j$ = 0 for each i, j whenever polynomials $f(x)\;=\;\sum_{i=0}^ma_ix^i$, $g(x)\;=\;\sum_{j=0}^mb_jx^j\;{\in}\;R[x]$ satisfy f(x)R[x]g(x) = 0. In this paper, we first extend the quasi-Armendariz property of semiprime rings to the skew polynomial rings, that is, we show that if R is a semiprime ring with an epimorphism $\sigma$, then f(x)R[x; $\sigma$]g(x) = 0 implies $a_iR{\sigma}^{i+k}(b_j)=0$ for any integer k $\geq$ 0 and i, j, where $f(x)\;=\;\sum_{i=0}^ma_ix^i$, $g(x)\;=\;\sum_{j=0}^mb_jx^j\;{\in}\;R[x,\;{\sigma}]$. Moreover, we extend this property to the skew monoid rings, the Ore extensions of several types, and skew power series ring, etc. Next we define $\sigma$-skew quasi-Armendariz rings for an endomorphism $\sigma$ of a ring R. Then we study several extensions of $\sigma$-skew quasi-Armendariz rings which extend known results for quasi-Armendariz rings and $\sigma$-skew Armendariz rings.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1150-1153
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• 2006

Many commercial high speed and lightly loaded rotating machineries incorporate floating ring bearings (FRBs) owing to their low cost and reduced power losses. Many researchers have developed various analytical models to predict the performance and the stability of those rotor-bearing systems with FRBs. However, most of the models failed to predict stability of the rotor-bearing systems with FRBs. FRBs comprise two fluid films in series and the ratio of floating ring speed to journal speed reflects the equilibrium state of the two fluid films. Therefore the speed ratio is one of the main concerns in the analysis of FRBs. This paper provides the experimental results of the speed ratio which enables one to verify of the analysis model for FRBs.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.289-309
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• 2019

This paper is intended as a discussion of some generalizations of the notion of a reversible ring, which may be obtained by the restriction of the zero commutative property from the whole ring to some of its subsets. By the INCZ property we will mean the commutativity of idempotent elements of a ring with its nilpotent elements at zero, and by ICZ property we will mean the commutativity of idempotent elements of a ring at zero. We will prove that the INCZ property is equivalent to the abelianity even for nonunital rings. Thus the INCZ property implies the ICZ property. Under the assumption on the existence of unit, also the ICZ property implies the INCZ property. As we will see, in the case of nonunital rings, there are a few classes of rings separating the class of INCZ rings from the class of ICZ rings. We will prove that the classes of rings, that will be discussed in this note, are closed under extending to the rings of polynomials and formal power series.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.23-27
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• 2004

We calculate dim $\hat{A}$ which is a completion of a Noetherian ring A with respect to I-adic topology. We do not use localization but power series techniques.